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KOGNITIVE

NEUROPHYSIOLOGIE DES

MENSCHEN

HUMAN COGNITIVE

NEUROPHYSIOLOGY

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ii Human Cognitive Neurophysiology 2011, 4 (1)

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2011, 4 (1) Kognitive Neurophysiologie des Menschen iii

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Pascual-Marqui, R., Michel, C., & Lehmann, D. (1994). Low resolution electromagnetic tomog-raphy: a new method for localizing electrical activity in the brain. International Journal ofPsychophysiology , 18, 49-65.

Zani, A., & Proverbio, A. (Eds.). (2002). The Cognitive Electrophysiology of Mind and Brain.San Diego: Elsevier.

iv Human Cognitive Neurophysiology 2011, 4 (1)

Inhalt — Contents

Inhalt — Contents

B. Kopp, C. Moschner & K. Wessel — Event-related Brain Potentials and the FunctionalSpecialization of Human Cerebral Hemispheres During Processing of Hierarchi-cal Visual Stimuli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

K. Schneider — Neuroimaging in German Court Rooms . . . . . . . . . . . . . . . . . 25T. Sauer — Time-Frequency Analysis, Wavelets and Why Things (Can) Go Wrong . . 38W. Skrandies — Abstracts of the 19th German EEG/EP Mapping Meeting . . . . . . . 65W. Skrandies – Electrical Neuroimaging (Book Review) . . . . . . . . . . . . . . . . . 83Announcements — Ankündigungen . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2011, 4 (1) Kognitive Neurophysiologie des Menschen v

B. Kopp et al. — Event-related Brain Potentials and the Functional Specialization of Human Cerebral Hemispheres

Abstract

B. Kopp, C. Moschner & K. Wessel (Braunschweig, Germany) — Event-related Brain Potentialsand the Functional Specialization of Human Cerebral Hemispheres During Processing of Hierar-chical Visual StimuliNeuropsychological evidence indicates that local and global features of visual stimuli are processed differ-

entially by the two cerebral hemispheres. Whereas local levels of hierarchical stimuli should be processed

more efficiently in the left hemisphere, the right hemisphere should be more efficient in processing global

information. Event-related brain potentials (ERPs) and lateralized readiness potentials (LRPs) were mea-

sured in a go-nogo task using hierarchical letters. Participants had to respond to conjunctions of target

shapes at global and local levels (i.e., a divided attention task). Responses were required only if target

features were met on both levels. Neither the behavioral results nor the ERP or LRP findings supported

global precedence, probably because the stimuli contained local, but not global, shapes at fixation, thereby

counteracting the usually faster global processing. ERPs provided evidence that the left and right parietal

regions were differentially activated during attentional allocation to the local and global levels, respec-

tively. Specifically, the posterior N2 at around 350 ms post-stimulus, but not the earlier exogenous ERP

components (P1, N1), showed the expected hemispheric lateralization. Response-locked ERPs manifested

a novel response-synchronized lateralized posterior positivity (rLPP) which peaked simultaneously with

the key-press. The rLPP may be an electrophysiological correlate of hemispheric monitoring.

Keywords: Lateralized event-related brain potentials (ERPs); Lateralized readiness potentials (LRPs);

Navon letters; Global precedence; Hemispheric specialization

Event-related Brain Potentialsand the Functional

Specialization of HumanCerebral Hemispheres During

Processing of HierarchicalVisual Stimuli

B. Kopp, C. Moschner & K. Wessel, CognitiveNeurology, University of Technology

Carolo-Wilhelmina, and Department ofNeurology, Braunschweig Hospital, 38126

Braunschweig, [email protected]

Introduction

Zaidel (2001) provided one of the best descrip-tions of hemispheric brain asymmetry: ”To-day, cerebral asymmetry remains a corner-stone of human neuropsychology and servesas a model system for a fundamental ques-tion in cognitive neuroscience: how do sep-arate subsystems of the mind/brain maintaintheir independence, on the one hand, and in-teract, on the other?” (p. 1322). In this ar-ticle, we address these questions by analyz-ing event-related brain potentials (ERPs; Luck,2005) recorded from healthy individuals duringprocessing of hierarchical visual stimuli.

2011, 4 (1) Kognitive Neurophysiologie des Menschen 1


Hemispheric specialization may be dividedby modality, material, or stage of processing,with the left hemisphere (LH) specialized forauditory, verbal or output processing and theright hemisphere (RH) for visual, nonverbal, orinput processing (cf., Corballis, 1997; Hugdahl& Davidson, 2003; Zaidel & Iacoboni, 2003).According to a widely held theory of hemi-spheric specialization, the LH is dominant forlanguage and praxis, whereas the RH is dom-inant for visuospatial functions. More recentviews describe hemispheric specialization interms of information-processing styles: the LHis analytic and the RH is holistic (cf., Robert-son & Ivry, 2000). Another view holds thatthe LH analyzes local and the RH analyzesglobal levels of hierarchical stimuli (Sergent,1982). In this context, the LH might be special-ized for processing relatively high spatial andtemporal frequencies whereas the RH mightbe specialized for relatively low frequencies(Hellige, 1993). According to the filtering-by-frequency hypothesis, the LH operates as ahigh-pass filter, allowing more high frequencyinformation to pass on for further processing,and the RH operates as a low pass-filter, al-lowing more low frequency information to passon for further processing (Ivry & Robertson,1998). Asymmetric frequency filtering yieldsnon-identical representations in the two hemi-spheres and, therefore, the two hemispheresare not simply performing redundant analy-ses: the LH representation should be moreefficient for identifying the local informationwhereas the RH representation should bemore efficient for identifying the global infor-mation in hierarchical perception tasks. Thehigh frequency/local vs. low frequency/globalhemispheric dissociation received empirical

support mainly from behavioral studies inhemisphere-damaged patients: Patients withlesions in the temporoparietal junction ex-hibited marked problems with the analysisof global aspects of such stimuli followingright-hemispheric lesions and with the analy-sis of local aspects following left-hemisphericlesions (Robertson, 1995; Robertson, Lamb,& Knight, 1988).

While in the real world global (e.g., a for-est) and local levels (e.g., the trees) of a visualscene are often quite different, most experi-mental studies of processing of hierarchical vi-sual stimuli have been composed of relativelysimilar elements at both levels. In particular,the hierarchical letter paradigm (Navon, 1977)is often used for investigating hemispheric spe-cialization of local processing and global pro-cessing: Large letters made up of small letters,like those shown in Figure 1, are presented tosubjects who are required to identify the large(global) letters or the small (local) letters, re-spectively. Response time (RT) studies usuallyreveal three effects: 1. A global precedenceeffect (also denoted level effect) because sub-jects usually respond to global shapes morerapidly than to local shapes (Miller & Navon,2002). 2. A congruency effect because con-gruent stimuli (e.g., a large H made of lit-tle „H“s) are easier to identify than incon-gruent stimuli (e.g., a large H made of lit-tle „E“s; Zaidel, Iacoboni, Zaidel, & Bogen,2003). 3. The congruency effect is, how-ever, asymmetric because conflicting informa-tion from an irrelevant global shape is disrup-tive when subjects discriminate among localshapes, whereas conflicting information fromirrelevant local shapes has little effect whensubjects discriminate among global shapes

2 Human Cognitive Neurophysiology 2011, 4 (1)


Figure 1: Columns show targets (leftmost column), global distractors (left column), local distractors

(right column), and standard distractors (rightmost column). Rows show the four possible ways to define

a particular stimulus set: Uppermost row: When the target (g+l+) equals the global and local “E”, the

global “E”, local “H” serves as global (g+l–) distractor, the global “H”, local “E” as local (g–l+) dis-

tractor, and the global and local “H” as standard (g–l–) distractor. Upper row: When the target (g+l+)

equals the global “E”, local “H”, the global and local “E” serves as global (g+l–) distractor, the global

and local “H” as local (g–l+) distractor, and the global “H”, local “E” as standard (g–l–) distractor.

Lower row: When the target (g+l+) equals the global “H”, local “E”, the global and local “H” serves

as global (g+l–) distractor, the global and local “E” as local (g–l+) distractor, and the global “E”, local

“H” as standard (g–l–) distractor. Lowermost row: When the target (g+l+) equals the global and local

“H”, the global “H”, local “E” serves as global (g+l–) distractor, the global “E”, local “H” as local

(g–l+) distractor, and the global and local “E” as standard (g–l–) distractor.



(Miller & Navon, 2002). Together, these phe-nomena are consistent with the hypothesisthat global information is available earlier thanlocal information (Miller & Navon, 2002).

RT studies provide, however, very limitedevidence for hemispheric specialization ofprocessing of hierarchical visual stimuli (vanKleeck, 1989; Yovel, Yovel, & Levy, 2001).A number of stimulus and task factors of hi-erarchical stimulus paradigms are known toinfluence hemispheric asymmetry:

1. When stimuli are presented either in theleft or right visual fields, hemispheric asymme-try is attenuated compared to central stimu-lus presentation (Han et al., 2002; Lux et al.,2004).

2. The nature of the stimulus material affectshemispheric asymmetry: Verbal stimuli (hier-archical letters) produce more pronounced evi-dence for hemispheric specialization than non-verbal (hierarchical figures) stimuli (Han, Fan,Chen, & Zhuo, 1997; Han, He, Yund, & Woods,2001).

3. Hemispheric asymmetry usually showsup in active cognitive tasks (Reinvang, Mag-nussen, & Greenlee, 2002), particularly whenthe task is attentionally demanding or com-putationally complex (Banich & Belger, 1990;Banich, 1998).

4. Stimulus congruency affects hemisphericasymmetry: Incongruent stimuli produce morepronounced evidence for hemispheric spe-cialization than congruent stimuli, particularlywhen response conflicts between the hierar-chical levels are implicated (Volberg & Hübner,2004). These authors attributed the effectof conflicting incongruency on hemisphericasymmetry to an elaborated stimulus rep-resentation which might be necessary for

resolving the response conflict induced bythese hierarchical stimuli.

5. Selective and divided attention affects thetemporal locus of hemispheric asymmetry dif-ferently, a phenomenon that we will discussbelow.

A method that has repeatedly been appliedto the investigation of hemispheric specializa-tion is the recording of ERPs. The ERP tech-nique offers measures of cortical activity withexcellent temporal resolution, even if events donot require behavioral responses (Luck, 2005).Three groups of ERP components may be dis-tinguishable on a relatively large scale:

1. Early components are related to sen-sory processing, with clearly modality-specificcharacteristics, and are often referred to asexogenous ERP components (P1, N1). How-ever, it should be stressed that pure top-downmechanisms, such as the voluntary allocationof visual spatial attention, can modulate theamplitude of exogenous components (Hillyard,Teder-Sälejärvi, & Münte, 1998). In contrast toprocesses related to spatial attention, the allo-cation of voluntary feature-based visual atten-tion modulates, in a more sustained manner,later parts of the ERP waveform at posteriorand anterior sites (P2, e.g., Potts, 2004).

2. Late ERP components show only min-imal modality-specific characteristics. There-fore, they are often referred to as endoge-nous components, and they are related to pro-cesses that are implicated in sensorimotor de-cisions (N2: Folstein & van Petten, 2008; P3:Kopp, 2008). Both endogenous ERP compo-nents should be subclassified into dissocia-ble anterior and posterior components: TheP3b component is a parietal positivity, peak-ing at approximately 400 ms after stimulus on-



set. It is larger to infrequent stimuli, particularlywhen these stimuli are targets (Picton, Lins,& Scherg, 1995). Instead, infrequent stimulithat are irrelevant to the task (distractors), butthat are more salient than the targets, evokethe P3a (Friedman, Cycowicz, Gaeta, 2001).The P3a has its peak earlier than the P3b, andit has a more frontocentral scalp distribution.The anterior N2 (here denoted N2c; Kopp,Rist, & Mattler, 1996) has a mediofrontal scalpdistribution, and peaks around 250-300 mspost-stimulus in tasks that utilize simple stim-uli. Attention-related N2 components have, inthe visual modality, a posterior scalp distribu-tion (Folstein & van Petten, 2008).

3. The readiness potential is a slow nega-tive potential that precedes spontaneous vol-untary movements of the distal limbs (Kornhu-ber & Deecke, 1965). The later part of theRP is larger over the contralateral scalp of amoved hand, and it arises mainly from primarymotor cortex (Lang et al., 1991). The lateral-ized portion of the readiness potential (LRP)can be measured in choice RT tasks in whicha stimulus signals that a response should bemade with one of two effectors, usually oneof the hands (Coles, 1989; Rinkenauer et al.,2004). LRP recordings are made from twoelectrode sites (C3 and C4) located over theleft and right hand areas of the motor cortex,respectively. Let the potentials recorded at thecontralateral and ipsilateral sites at time tbedenoted as Contralateral(t) and Ipsilateral(t)to the responding hand. The LRP at time tisthen defined as LRP (t) = Average over hands[Contralateral (t) – Ipsilateral (t)]. The result-ing LRP will be negative when the response isperformed with the signaled hand, but it will bepositive when the response is performed with

the wrong hand.

There are several main findings from ERPstudies of processing of hierarchical visualstimuli:

1. Selective vs. divided attention tasks ledto a dissociation with regard to the P1 compo-nent of the ERP: The P1 component was notdifferent for global versus local targets underconditions of divided attention. But under se-lective attention conditions, the P1 componentwas enlarged for global versus local attention(Heinze, Hinrichs, Scholz, Burchert, & Man-gun, 1998). Similar results were obtained forthe N1 component (Proverbio, Minniti, & Zani,1998).

2. The posterior N2 component of the ERPshowed the expected hemispheric asymme-tries, i.e. a relatively larger amplitude overthe left hemisphere for local targets and overthe right hemisphere for global targets (Heinze& Münte, 1993; Heinze et al., 1998; Mali-nowski, Hübner, Keil, & Gruber, 2002; Vol-berg & Hübner, 2004; Yamaguchi, Yamagata,& Kobayashi, 2000; Yoshida, Yoshino, Taka-hashi, & Nomura, 2007). While one cannot as-sume that potentials over one hemisphere arenecessarily generated in the underlying hemi-sphere, these data showed differential lateral-ization of local and global visual processing.

3. The LRP received relatively little consid-eration. In Experiment 1 of Miller & Navon’s(2002) study, subjects responded to localshapes and ignored global shapes (selectiveattention). As revealed by the LRP, the ir-relevant global shapes activated responsesin the motor cortex. In Experiment 2, sub-jects responded to conjunctions of targetshapes at local and global levels (dividedattention), while withholding the response if



the target shape appeared at only one level(i.e. a go-nogo task). Global, but not local,target shapes activated responses. TheseLRP results substantiate global precedence.However, another LRP study (Ridderinkhof &van der Molen, 1995), in which no RT globalprecedence effect became apparent, revealedthat the level effect varies as a function of thetemporal advantage for the processing of infor-mation from either level: The individually faster(local or global) level interferes with the slowerlevel, but it is immune to such interferencefrom the slower level.

Together the ERP findings indicate that, atleast under conditions of divided attention,early sensory inputs are not modulated togate global versus local information differen-tially into the two hemispheres. Rather, laterstages of processing that may be asymmet-rically organized in the left and right hemi-spheres operate in parallel to process globaland local aspects of hierarchical stimuli (c.f.the posterior N2 effect of the ERPs). This pat-tern of results supports models proposing thatspatial frequency analysis is only asymmet-ric at higher stages of perceptual processingand not at the earliest stages of visual corticalanalysis (Sergent, 1982; Hellige, 1993; Ivry &Robertson, 1998). The available LRP resultsshow that the processing of information fromthe faster (usually, but not always, the global)level interferes with the slower level wheneverthe fast level activates the conflicting responsein the motor cortex.

The present study aimed at an electrophys-iological analysis of global precedence andhemispheric asymmetry. The study madeuse of an adaptation of the hierarchical let-ter paradigm (Navon, 1977) which was akin

to Miller and Navon’s (2002) which combinedthe demand to divide attention and to decidewhether or not one has to respond (i.e, a go-nogo task). A set of four hierarchical stimulilike those shown in Figure 1 were presented.This set was produced by factorially combiningtwo letter shapes (namely, E and H) at two hi-erarchical levels (local, global). Subjects hadto respond to conjunctions of target shapesat local and global levels, while withholdingthe response when the target shape appearedat only the local or the global level, respec-tively, or when the target shape appeared atnone of the levels. The presence of responseconflicts can be evaluated by comparing cor-tical responses in response to global and lo-cal distractors, respectively, with cortical re-sponses in response to standard distractors(cf. Figure 1). Specifically, the global – stan-dard comparison allows to evaluate the inter-ference effect induced by target compatibilityat the global level, whereas the local – stan-dard comparison allows to evaluate the inter-ference effects induced by target compatibilityat the local level. It is worth noting, however,that it is the target-incompatible level of thesehierarchical stimuli which implies to withholdthe response (i.e., the local level of the globaldistractor and the global level of the local dis-tractor).

The global precedence hypothesis leads tothe prediction of larger interference effects byglobal distractors in comparison to local dis-tractors. It is not possible to analyze RTeffects in this study because the distractorsare presented in nogo trials. Yet, the ex-periment could provide information about theglobal precedence effect. First, ERPs of-fer measures of cortical activity with excel-



lent temporal resolution (Luck, 2005). Ourgroup described ERP results that were ob-tained from non-hierarchical versions of thisgo-nogo task in two earlier publications (Kopp,Tabeling, Moschner, & Wessel, 2007; Kopp& Wessel, 2010). Specifically, an enhancedanterior N2 (N2c) and an enhanced anteriorP3 (P3a) were observed when an easily dis-criminated attribute activated the go response,whereas a less easily discriminated attributeimplied to withhold the response. Second,when the response has to be made with onehand, but in other parts of the experiment withthe other hand, the LRP provides informationwhether level-specific target compatible infor-mation led to response activation. These nogotrials should provide a sensitive test for globaland/or local response activation because inthese nogo trials no response-related LRP isgenerated to obscure the level-specific pre-liminary response activation (Miller & Navon,2002).

With regard to hemispheric asymmetry, theglobal distractor is expected to be preferablyprocessed in the left hemisphere. This is be-cause it is the local, target-incompatible infor-mation that drives the nogo decision. The cor-rect decision requires an elaborated local rep-resentation (Volberg & Hübner, 2004) which isexpected to be located within the left hemi-sphere (Sergent, 1982; Hellige, 1993; Ivry &Robertson, 1998). In contrast, the local dis-tractor is expected to be preferably processedin the right hemisphere. Here, it is the global,target-incompatible information that drives thenogo decision. The correct decision requiresan elaborated global representation (Volberg &Hübner, 2004) which is expected to be locatedwithin the right hemisphere (Sergent, 1982;

Hellige, 1993; Ivry & Robertson, 1998).

Methods

Participants

Twenty-four volunteers participated (M = 22years; range = 18-39 years; four males;twenty-two right-handed). All participantswere un-medicated and neurologically unim-paired. All had normal or corrected-to-normalvision and normal hearing. All participantswere students at the University of Technologyat Braunschweig. They were compensatedwith course credits. A written consent state-ment was obtained from participants after thenature and objectives of the experiment wereexplained.

Stimuli

Navon figures (large, global letters made upof small, local letters) were created within a4 × 7 matrix (Figure 1). Two different let-ters (E, H) were used to create the stimuli.There were four different stimuli: global shape“E” and local shape “E”, global shape “E” andlocal shape “H”, global shape “H” and localshape “E”, as well as global shape “H” andlocal shape “H”. The letters were displayedin black against white background. Stimuli(150 ms duration) and a preceding (red) fix-ation star (250 ms duration; 0.3˚ visual an-gle) were presented centrally. The visual an-gles subtended by the global and local letterswere: 6.6˚ (global letter – vertical axis), 3.3˚(global letter – horizontal axis), 0.8˚ (local let-ter – vertical axis), 0.6˚ (local letter – horizon-tal axis). Viewing distance was 125 cm. Thestimuli were presented one at a time in the



center of a computer screen (FlexScan T76619“(Eizo, Hakusan, Ishikawa, Japan); 1280 ×1024 pixels at 100 Hz presentation rate; 1150ms inter-stimulus-interval). Stimulus presenta-tion was controlled by the Presentation R© soft-ware (Neurobehavioral Systems, Albany, CA)that was installed on an IBM- compatible per-sonal computer.

Apparatus and Procedure

Participants were instructed that one stimuluswas the target (denoted g+l+, i.e., the stim-ulus with the target-compatible global shapeand with the target-compatible local shape; cf.Figure 1) throughout the experiment. In anygiven trial, one out of the four stimuli was pre-sented and participants had to decide whetheror not the current stimulus equaled the target.Participants pressed the space bar with theirindex finger on a standard computer keyboardwhen they recognized the target stimulus. Par-ticipants were instructed not to respond if thestimulus was recognized as one of the distrac-tors. No feedback about response accuracywas provided.

There were three types of distractors, theglobal distractor, g+l–, the local distractor, g–l+, and the standard distractor, g–l–. Individ-ual participants received different stimuli as thetarget stimulus, i.e. the global “E” / local “E”,the global “E” / local “H”, the global “H” / local“E”, or the global “H” / local “H”, respectively.Adequate counterbalancing (i.e., six partici-pants received each of these types of stimulias the target) yielded targets and distractorsthat were, on average, composed of physicallyidentical stimuli (cf. Figure 1). Thus, com-parisons between averaged ERPs in responseto the various distractor types avoid physical

stimulus confounds (Luck, 2005).Each participant performed eight blocks of

144 trials each (8 × 144 = 1152 trials over-all). Blocks were divided by short breaks (last-ing two or three minutes). The four stimulioccurred with equal probabilities within eachblock (i.e., in 144 / 4 = 36 trials per block).The order of succession of stimuli was pseudo-random. Response hand (left, right) was al-ternated. The responding hand was main-tained across four consecutive blocks. The or-der of succession of the responding hand wascounterbalanced across participants. Withineach level of response hand, each stimulus oc-curred in 144 (4 × 36) trials.

Participants were instructed that they wouldreceive four different types of stimuli in rapidsuccession, and that one of these stimuliwould be their target throughout a block oftrials. They were informed about the random-ness of the stimulus sequence, and they wereasked to respond as fast as possible with-out committing errors. Participants receivedtwenty-four practice trials in the run-up to theexperiment. The target detection task that wasperformed on the practice stimuli was basedon the number (one or two) and the spatialorientation (towards the left or towards theright) of green bars.

Recording

Continuous EEG was recorded by meansof another IBM-compatible personal com-puter, a QuickAmps-72 amplifier (BrainProducts, Gilching, Germany) and theBrainVisionRecorder R© software (Brain Prod-ucts, Gilching, Germany) from frontal (F7, F3,Fz, F4, F8), central (T7, C3, Cz, C4, T8), pari-etal (P7, P3, Pz, P4, P8), occipital (O1, O2),



and mastoid (M1 (TP9), M2 (TP10)) sites.Ag-AgCl EEG electrodes were used. Theywere mounted on an EasyCap (EasyCap,Herrsching-Breitbrunn, Germany). Electrodeimpedance was kept below 10 kΩ. All EEGelectrodes were referenced to average refer-ence. Participants were informed about theproblem of non-cerebral artifacts and theywere encouraged to reduce them (Picton etal., 2000). Ocular artifacts were monitored bymeans of bipolar pairs of electrodes positionedat the sub- and supraorbital ridges (verticalelectrooculogram, vEOG) and at the externalocular canthi (horizontal electrooculogram,hEOG). The EEG and EOG channels wereamplified with a bandpass of 0.01 to 30 Hzand digitized at 250 Hz.

Offline analysis was performed by means ofthe BrainVisionAnalyzer R© software (BrainProducts, Gilching, Germany). Semi-automated artifact rejection was performedbefore averaging to discard trials during whichan eye movement or any other non-cerebralartifact occurred (maximum allowed voltagestep per sampling point: 50 µV; maximumallowed amplitude difference: 200 µV; mini-mum allowed amplitude: -200 µV; maximumallowed amplitude: 200 µV; lowest allowedactivity (max-min, interval length 100 ms):0.5µV). Ocular correction included semi-automatic blink detection and the applicationof an established method for ocular artifactremoval (Gratton, Coles, & Donchin, 1983).

The EEG was then divided into epochs of1000 ms duration, starting 100 ms before theonset of stimuli. Error trials (misses, falsealarms) were excluded from analysis (misseswhen the stimulus was a target, false alarmswhen the stimulus was a distractor). Next,

the pre-stimulus baseline of 100 ms was sub-tracted from the sampling points. Deflectionsin the averaged EOG waveforms were small,which indicated good maintenance of fixation.No digital filtering was applied to the data.

Data analysis

Behavioral task performance was quantifiedin two ways: Firstly, the median of the re-sponse speed at each level of response handwas computed for each individual participant,and these median individual response times(RTs) were subjected to statistical analysis.Secondly, the accuracy of the behavioral re-sponses was computed at each level of re-sponse hand for each individual participant.The percentage of hits was computed for thetarget stimuli (g+l+). Percentages of correctrejections were separately computed for eachdistractor type. Finally, the percentage of cor-rect rejections was computed as an averageacross all three distractor types. These per-centage values were arcsin transformed priorto statistical analysis.

Peak amplitudes of the P1 in response tothe targets and to the distractors were mea-sured at latency 88 ms with respect to the pre-stimulus baseline period at occipital electrodes(i.e., the peak latency of the P1 in the grand-average, cf. Figure 4; this and all following la-tencies were determined after inspection of theindividual and group grand averages). Peakamplitudes of the N1 in response to the tar-gets and to the distractors were measured atlatency 160 ms (i.e., the peak latency of theN1 in the grand-average, cf. Figure 4) with re-spect to the pre-stimulus baseline period at oc-cipital electrodes. Peak amplitudes of the P3bin response to the targets and to the distrac-



tors were measured at latency 432 ms (i.e., thepeak latency of the P3b in the grand-average,cf. Figure 2) with respect to the pre-stimulusbaseline period at electrode Pz at which theP3b was maximal. The analysis of the anteriorP2, of the anterior and posterior N2 and of theP3a are described in detail in the Results. Theanalysis of the LRP followed the specificationsthat were described in the Introduction.

Performance measures and the ERP am-plitude measures were subjected to repeatedmeasures analyses of variance (ANOVAs) us-ing the Greenhouse-Geisser correction. Theresults of the univariate tests are provided, us-ing a format which gives the uncorrected de-grees of freedom, and ε (Picton et al., 2000).A significance level of α = 0.01 was fixed.

Results

Behavioral data

Response speed and response accuracy aredocumented separately for left hand and righthand responses in Table 1. RT measureswere analyzed by a one-way hand (left, right)ANOVA, F (1, 23) < 1, p = 0.85.1 Participantsperformed the required classification at a near-perfect level, as revealed by the hit rates (bothmeans > 99.5%) and by the correct rejectionrates (all means > 98.8%). Another one-wayANOVA revealed that hand (left, right), F (1,23) < 1, p = 0.51, did not affect hit rates.When the correct rejection rates of the varioustypes of distractors were tested in a two-waystimulus category (global distractor, local dis-tractor, standard distractor) × hand (left, right)ANOVA, the stimulus category main effect,F(2, 46) = 10.9, p = 0.001, ε = 0.73, but nei-ther the hand main effect, F (1, 23) = 1.1, p =

0.30, nor the interaction between stimulus cat-egory and hand, F (2, 46) < 1, p = 0.77, ε =0.99, proved significant. Simple contrasts re-vealed that the correct-rejection rates relatedto the local distractor were slightly lower thanthe correct rejection rate related to the globaldistractor, F (1, 23) = 11.4, p < 0.004, as wellas to the standard distractor, F (1, 23) = 4.6,p < 0.05. These behavioral results show thatthere was a small, yet significant, decrease ofcorrect rejections in response to the local dis-tractors compared to the global and standarddistractors, respectively. The finding of a se-lective increase of false alarms in response tolocal distractors is consistent with the conclu-sion that the availability of local information,wrongly implying a go decision, tended to ex-ceed the availability of global information, cor-rectly implying a nogo decision.

Global precedence

Stimulus-locked ERP

The left panel of Figure 2 plots grand-averageERPs at midline electrodes that were obtainedin response to target stimuli as well as in re-sponse to global, local, and standard distrac-tors. Target stimuli evoked a significantly largerP3b with parietal maximum (+7.4 µV peak am-plitude at Pz) compared to the global (+3.6µV peak amplitude at Pz), the local (+3.8 µVpeak amplitude at Pz), or the standard dis-tractor (+2.7 µV peak amplitude at Pz). Thepresence of a prominent target-P3b at Pz wasconfirmed by a two-way stimulus category (tar-get, global distractor, local distractor, standarddistractor) × hand (left, right) ANOVA, yieldinga highly reliable stimulus category effect, F (3,69) = 48.1, p < 0.001, ε = 0.60. Simple con-



Table 1: Response speed and response accuracy as a function of responding hand.

left right

M SD M SD

RT (ms) 488 36 489 51

Hits 99.7 .6 99.5 .8

CR (g+l-) 99.3 1.0 99.1 1.3

CR (g-l+) 99.0 1.2 98.8 1.3

CR (g-l-) 100 .1 99.9 .2

Note. RT, response time; hits (in percent); CR, correct rejections (in percent). g+l- = global distractor; g-l+ = local

distractor; g-l- = standard distractor.

trasts revealed that the target P3b was largerthan any distractor P3b (target vs. global dis-tractor: F (1, 23) = 58.9, p < 0.001; target vs.local distractor: F (1, 23) = 45.4, p < 0.001; tar-get vs. standard distractor: F (1, 23) = 71.4, p< 0.001).

Difference waveforms at midline electrodeswere computed as ERP indices of globalprecedence. Specifically, difference wavesbetween global and standard distractor ERPs(see the left panel of Figure 2) and differencewaves between local and standard distractorERPs (see the left panel of Figure 2) werecalculated (see the right panel of Figure 2).The statistical analysis of the differenceswaves relied on the calculation of mean am-plitudes within 50 ms bins (time intervals)across the waveforms. Three-way stimuluscategory (global/standard distractor differ-ence, local/standard distractor difference) ×hand (left, right) × electrode site (Fz, Cz, Pz)ANOVAs yielded significant deviation of the dif-ference waves from zero in the 200 (175-225)ms, 400 (375-425) ms, 450 (425-475) ms, 500(475-525) ms, and 550 (525-575) ms bins (allF ‘s > 10.2, all p-values < 0.004). The earlypositive deflection around 200 ms indicatesa more prominent anterior P2 in response to

the global and local distractors in comparisonto the standard distractor, whereas the laterpositive deflection between 400 ms to 550 msindicates a more prominent P3a in response tothe global and local distractors in comparisonto the standard distractor. The finding thatno negative deviation of the difference wavesfrom zero was discernible is consistent withthe conclusion that the anterior N2 was equallyprominent in response to global or local dis-tractors in comparison to standard distractors.Importantly, stimulus category affected the dif-ference waves solely in the 650 (625-675) ms,700 (675-725) ms, and 750 (725-775) ms bins(all F -values > 13.1, all p-values < 0.001).2

These ERP results show that the time courseand the magnitude of the anterior P2 and theP3a were indistinguishable in response to theglobal and the local distractors, respectively.

Stimulus-locked LRP

As shown in Figure 3, there was a distinct neg-ative dip in the stimulus-locked LRP (sLRP) inresponse to target stimuli approximately 350ms after stimulus onset. To verify this LRP sta-tistically, mean sLRP amplitude was computedduring 50 ms bins, starting 50 ms and ending



Figure 2: Left panel. Stimulus-locked grand-average ERPs at midline electrodes that were obtained in

response to targets (g+l+), global distractors (g+l–), local distractors (g–l+) and standard distractors

(g–l–). Right panel. Difference waveforms at midline electrodes, i.e. difference waves between global and

standard distractor ERPs ((g+l–)-(g–l–)), and difference waves between local and standard distractor

ERPs ((g–l+)-(g–l–)).



Figure 3: Stimulus-locked LRPs (sLRP) that were obtained in response to targets (g+l+), global distrac-

tors (g+l–), local distractors (g–l+) and standard distractors (g–l–).

800 ms after stimulus onset. The first bin inwhich this amplitude was significantly less thanzero was the 350 ms bin, F (1, 23) = 19.9, p< 0.001. The sLRP waveform remained belowzero in all later bins, without exception (F ‘s >13.1, all p-values < 0.001).

Next, stimulus-locked LRPs in response tothe distractors were analyzed (see Figure 3).Inspection of Figure 3 reveals that distractorsdid not elicit noticeable negative dips. The sta-tistical analysis of the LRPs relied on the cal-culation of mean amplitudes within 50 ms binsacross the waveforms. One-way stimulus cat-egory (global distractor, local distractor, stan-dard distractor) ANOVAs yielded positive de-viation of the LRPs from zero in the 350 (325-375) ms, 400 (375-425) ms, 450 (425-475) ms,and 500 (475-525) ms bins. All other effects,and specifically all stimulus category effects,fell below significance (remaining intercept ef-fects: F ‘s < 6.9, all p-values > 0.015); all stim-

ulus category effects: F ‘s < 1.1, all p-values >0.34). These LRP results suggest that none ofthe distractors was associated with noticeableresponse activation, as would be reflected by anegative dip in the LRP. Furthermore, the tonicpositive deflection of the LRPs possibly indi-cates functional deactivation of the contralat-eral motor areas in the time bin between 350ms and 500 ms.

Hemispheric asymmetry

Stimulus-locked ERP

Figure 4 plots grand-average ERPs at lateralfrontal and occipitoparietal electrodes, sepa-rately for target stimuli as well as for global,local, and standard distractors. A three-waystimulus category (target, global distractor, lo-cal distractor, standard distractor) × hand (left,right) × hemisphere (left, right) ANOVA wasperformed on P1 and N1 peak amplitudes at



Figure 4: Stimulus-locked grand-average ERPs at lateral electrodes that were obtained in response to

targets (g+l+), global distractors (g+l–), local distractors (g–l+) and standard distractors (g–l–).

occipital electrodes. With regard to the P1 am-plitude, no main or interaction effect attainedstatistical significance (all F -values < 4.4, allp-values > 0.017). With regard to the N1 am-plitude, no main or interaction effect attainedstatistical significance (all F -values < 4.1, allp-values > 0.055). Together these results in-dicate that early visual cortical processing wasnot affected by stimulus category, hemisphereor responding hand, nor by their interactions.

Two-way hand (left, right) × region (ante-rior, posterior) ANOVAs were performed on thedouble subtraction waveforms (cf. legend ofFigure 5). The results on the intercept areof particular importance because they indicatebins during which a reliable deviation of the dif-ference waveforms from zero was observed. Anegative deflection in these difference wave-forms occurred exclusively in the 350 ms bin,

F (1, 23) = 9.4, p = 0.006.3 A conventional four-way region (frontocentral, parietooccipital) ×stimulus category (global distractor, local dis-tractor) × hand (left, right) × hemisphere (left,right) ANOVA on the mean ERP amplitudes(posterior N2) in the 350 (325 – 375) ms binrevealed a significant main effect of region, F(1, 23) = 33.8, p < 0.001, and a significant in-teraction between stimulus category and hemi-sphere, F (1, 23) = 9.3, p < 0.01, whilenone of the remaining main effects or inter-action effects reached statistical significance(all F -values < 6.6, all p-values > 0.017). Al-though the interaction between region, stimu-lus category and hemisphere failed to reachstatistical significance, inspection of the differ-ence waves suggested a parietal maximum ofthe stimulus category × hemisphere interac-tion. An additional three-way stimulus cate-



Figure 5: Stimulus-locked double subtraction waveforms obtained at eight electrode pairs. Double sub-

traction waveforms were computed as ERP indices of hemispheric asymmetry. Specifically, hemispheric

ERP differences were computed, i.e. ERP at left electrodes – ERP at homologous right electrodes (an-

terior region: F7 – F8, F3 – F4, C3 – C4, T7 – T8; posterior region: P7 – P8, P3 – P4, O1 – O2,

TP9 – TP10), separately for global and local distractors. Next, the difference global distractors – lo-

cal distractors of the hemispheric ERP differences was computed, a procedure which mainly tests for

algebraic sign differences of hemispheric ERP differences. In particular, if the hemispheric differences

are negative in case of the global distractor, whereas these are positive in case of the local distractor,

the difference between a negative value and a positive value will yield a strongly negative value, and

indicating a cross-over of hemispheric lateralization. Mean amplitudes of this measure were computed

for 50 ms bins, starting 50 ms and ending 800 ms ms after stimulus onset. The inlet (left panels) shows

the grand-average ERPs at parieto-lateral electrodes (P7, P8) that were obtained in response to global

distractors (g+l–, solid lines) and local distractors (g–l+, dashed lines).



gory (global distractor, local distractor) × hand(left, right) × hemisphere (left, right) ANOVAon the mean ERP amplitudes (posterior N2) atthe lateral parietal electrodes (P7, P8) in the350 (325 – 375) ms bin yielded a significantstimulus category × hemisphere interaction, F(1, 23) = 8.1, p < 0.007, while none of theremaining main effects or interaction effectsreached statistical significance (all F -values <6.7, all p-values > 0.016).

The stimulus category × hemisphere inter-action for the amplitude of the posterior N2can be easily identified in Figure 5. Inspec-tion of the inlet reveals that the global distrac-tor evoked a more negative ERP wave at P7(over the left hemisphere) in the latency rangeof the posterior N2, whereas the local distrac-tor elicited a slightly more negative ERP waveat P8 (over the right hemisphere) in the latencyrange of the posterior N2. While one cannotassume that potentials over one hemisphereare necessarily generated in the underlyinghemisphere, this pattern of hemispheric later-alization seems to be consistent with the pre-dicted hemispheric asymmetry. Specifically, asoutlined in the introduction, the global distrac-tor is expected to be preferably processed inthe left hemisphere, whereas the local distrac-tor is expected to be preferably processed inthe right hemisphere.

Response-locked ERP

Figure 6 shows the scalp topography of theresponse-locked ERPs in response to targetstimuli, separately for right- and left-hand re-sponses. With regard to the lateralization ofthe ERPs, three observations are noteworthy:First, an anterior contralateral negativity oc-curred at electrodes C3 and C4 as well as F3

and F4. The anterior contralateral negativity atC3 and C4 gives rise to the response-lockedLRP (rLRP) once the contralateral – ipsilateraldifference is averaged over the two respond-ing hands. As shown in Figure 7, there was adistinct negative deflection in the rLRP approx-imately 150 ms before the response. To verifythis negative rLRP dip statistically, mean rLRPamplitude was computed during 50 ms bins,starting -450 (i.e., the -475 – -425 ms bin) msbefore the response and ending +450 (i.e., the+425 – +475 ms bin) ms after the response.The first bin during which this amplitude wassignificantly less than zero was the -150 msbin, F (1, 23) = 22.6, p < 0.001. The rLRPwaveform remained below zero in all later bins(all F -values> 26.5, all p-values< 0.001), withtwo noteworthy exceptions: 1. There was asharp positive peak in the rLRP waveform atthe time of the response (see Figure 7), andthe mean rLRP amplitude in the 0 ms bin didnot differ statistically from zero, F (1, 23) = 6.9,p = 0.015. 2. There was a later positive peakin the rLRP waveform (see Figure 7), and themean rLRP amplitude in the 100 ms bin and inthe 150 ms bin did not differ statistically fromzero (all F -values < 2.8, all p-values > 0.11).

Second, a contralateral positive peakemerged at posterior electrodes that peakedat the time of the response. Inspection ofFigure 7 reveals that this contralateral pos-itive peak had a parietocentral topography,in contrast to the frontocentral topography ofthe rLRP. One-way region (frontal, average ofthe F7/F8 and F3/F4 electrode pairs; parietal,average of the P7/P8 and P3/P4 electrodepairs, occipitotemporal, average of the O1/O2and TP9/TP10 electrode pairs) ANOVAs werecomputed for mean amplitudes within 50 ms



Figure 6: Response-locked grand-average ERPs in response to targets, separately for left and right hand

responses. rLRP: response-locked lateralized readiness potential; rLPP: response-locked lateralized

posterior positivity; hEOG: horizontal electrooculogram.

bins across the waveforms. Region affectedthe waveforms in the -100 ms and all later bins(all F -values > 6.0, all p-values < 0.005), withtwo exceptions (100 ms bin: F (2, 46) < 1;200 ms bin: F (2, 46) = 2.3, p = .12). Thewaveforms were positively deflected in the 0ms (F (1, 23) = 32.6, p < .001) and 150 ms (F(1, 23) = 13.6, p < .002) bins, whereas startingwith the 350 ms bin, a negative deflection ofthe waveforms became apparent (all F -values> 17.1, all p-values < 0.001).4

Discussion

The present data are inconsistent with thepredictions that were derived from the globalprecedence hypothesis. Specifically, the am-plitudes of the anterior N2 (N2c) and of theanterior P3 (P3a) did not differ between local

and global distractors. In addition, the sLRPobtained in nogo trials did not indicate sub-stantial preliminary response activation by lo-cal distractors or by global distractors. In con-trast, the present data are consistent with thepredictions that were derived from the hypoth-esis of hemispheric asymmetry. Specifically,the posterior N2 showed the expected patternof hemispheric lateralization. In addition, weobserved a new, response-locked lateralizedposterior positivity (rLPP) that might provide aclue towards hemispheric interaction. We dis-cuss issues related to the global precedencehypothesis and issues related to hemisphericasymmetry separately in the following para-graphs.



Figure 7: Response-locked double subtraction waveforms obtained at eight electrode pairs. At C3/4, the

resulting difference wave equals the rLRP. At posterior electrode pairs, a novel contralateral positive

peak emerged (rLPP, response-locked lateralized posterior positivity). Note, that the rLRP at C3/4 and

the rLPP seem to overlap.



Global precedence

As outlined in the introduction, the globalprecedence hypothesis led to the prediction oflarger interference effects by global distractorsin comparison to local distractors. Specifi-cally, an enhanced anterior N2 (N2c) and anenhanced anterior P3 (P3a) in response toglobal distractors compared to local distrac-tors were expected. Furthermore, the sLRPobtained in these nogo trials provided a testfor preliminary global and/or local responseactivation, with the expectation that globalresponse activation should exceed local re-sponse activation. None of these predictedERP (N2, P3, sLRP) effects showed up inthe present experiment. Instead, our resultsindicate that preliminary response activationby global information equaled preliminaryresponse activation by local information.

There are at least two possible reasons forthe absence of a global precedence effect. 1.Global precedence may not be obtained whenstimuli contain local, but not global, shapes atfixation. It has been argued that local shapesat fixation confound stimulus level with eccen-tricity (Miller & Navon, 2002; Navon, 1977).If local features at fixation were more easilydiscriminable than local shapes at other loca-tions in the visual field or than global shapes,this discriminability advantage could counter-act the typical speed advantage for global in-formation. 2. Participants in Ridderinkhof &van der Molen’s (1995) study performed a two-choice task. Participants in Miller & Navon’s(2002) experiments had to solve left/right/nogotasks, i.e. they chose between left hand re-sponse, right hand response and no responsewithin each trial. Participants in our experi-ment chose between left hand response and

no response as well as between right hand re-sponse and no response within different blocksof trials. These decisional discrepancies mightalso have contributed to the heterogeneity ofthe reported results (cf., Introduction).

We described ERP results in two earlierpublications that were obtained from non-hierarchical versions of this go-nogo task.Color and shape were the stimulus attributesin our first study (Kopp et al., 2007). Stimuluscolor, but not stimulus shape, led to responsepreparation (as indicated by ERP measures)when color was easily discriminated. In con-trast, color did no longer induce responsepreparation when the color discriminationswere more difficult. In the second study (Kopp& Wessel, 2010), stimulus size, but not stimu-lus shape, led to response preparation whensize could be easily discriminated. When sizediscriminations were more difficult, stimulusshape, but not stimulus size, led to responsepreparation. Thus, we reported electrophys-iological evidence that response preparationcan be carried out in parallel with stimulusrecognition based on preliminary output fromperceptual processes, before stimulus recog-nition is complete. In the present study, thesLRP findings indicate that preliminary re-sponse activation was not detectable in nogotrials.

Hemispheric asymmetry

Our results clearly support earlier ERP stud-ies on hemispheric asymmetry. As in ear-lier divided attention paradigms (Heinze et al.,1998; Proverbio et al., 1998), early visual cor-tical processing, as indicated by the P1 andN1 ERP components, was not influenced byany of the experimental factors (stimulus cate-



gory, hemisphere or responding hand). Thus,at least under conditions of divided attention,early sensory inputs are not modulated togate global versus local information differen-tially into the two hemispheres.

The posterior N2 component of the ERP(Folstein & van Petten, 2008) showed the ex-pected hemispheric asymmetry, i.e. a rela-tively larger amplitude over the left hemispherefor global distractors and over the right hemi-sphere for local distractors. These data showdifferential lateralization of local and global vi-sual processing (see also Heinze & Münte,1993; Heinze et al., 1998; Malinowski et al.,2002; Volberg & Hübner, 2004; Yamaguchi etal., 2000; Yoshida et al., 2007). The hemi-spheric asymmetry of the posterior N2 ap-peared in a temporally and topographically dis-tinct manner. Specifically, we observed asym-metrical N2 amplitudes in the latency rangearound 350 ms following stimulus onset, withparietal maximum.

These posterior N2 findings indicate thatlater stages of processing are asymmetricallyorganized in the left and right hemispheres andoperate in parallel to process global and lo-cal aspects of hierarchical stimuli. This pat-tern of results supports models proposing thatspatial frequency analysis is only asymmet-ric at higher stages of perceptual processingand not at the earliest stages of visual corticalanalysis (Sergent, 1982; Hellige, 1993; Ivry &Robertson, 1998). There is, however, a caveatwhich should be mentioned here because ver-bal stimuli (hierarchical letters) produce morepronounced evidence for hemispheric special-ization than do nonverbal (hierarchical figures)stimuli (Han et al., 1997, 2001). Therefore, areplication study, based on nonverbal stimuli,

seems desirable. Furthermore, the use of mul-tiple statistical tests demands caution in inter-pretation.

An unexpected, novel finding was theidentification of the rLPP. The rLPP reflectsresponse-locked, asymmetrical cortical ac-tivity, with a parietal topography. We haveargued above that our (and others) ERP re-sults indicate that each hemisphere performsits specialized processing, that this process-ing occurs in parallel, and that the results ofthis processing are simultaneously available.Thus, in this type of divided attention, hierar-chical visual perception tasks, local and globalinformation are concurrently available and aredistinctively distributed across hemispheres.

Under these circumstances, efficient per-formance monitoring hinges upon interhemi-spheric interaction. Zaidel (1987) formulatedthe hypothesis of hemispheric monitoring: Al-though each hemisphere contains its own per-formance monitor, each hemisphere can alsomonitor the other. Thus, it becomes possi-ble for one hemisphere to monitor the resultsof processing in the other hemisphere. Todate, however, there is no empirical evidenceto support Zaidel’s hypothesis (Hochman &Eviatar, 2004, 2006). Hemispheric monitor-ing should be advantageous whenever elabo-rated stimulus representations are distributedacross hemispheres. Therefore, it is an in-triguing possibility that the rLPP indicates per-formance monitoring across hemispheres, al-beit this assertion remains by nature some-what speculative. If this interpretation of therLPP is correct, our data suggest that hemi-spheric monitoring takes place at a relativelylate stage of information processing. Specifi-cally, hemispheric monitoring, as possibly indi-



cated by the rLPP, seems to be time-locked tothe execution of the response.

Here, we presented evidence that the leftand right hemisphere preferentially perform ei-ther local or global processing, respectively,and that this processing occurs in parallel. Theresults of this processing are simultaneouslyavailable in the present hierarchical visual per-ception task, without global precedence. TheERP findings indicated hemispheric special-ization at a relatively late stage of processing.Furthermore, we suggest that this task pro-vides an instance for investigating collabora-tion between hemispheres. Specifically, hemi-spheric monitoring, hitherto a purely theoreti-cal construct, may become an empirically ad-dressable characteristic of interhemispheric in-teraction.

Acknowledgements

We thank Jasmin Kizilirmak and Carolin Lieb-scher for their help in data acquisition and dataanalysis.

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Footnotes

1Half of the subjects responded to congruent targetsand the other half responed to incongruent targets. How-ever, RTs were not influenced by the congruency of thetarget stimulus (congruency main effect, F (1, 22) < 1, p= .71; interaction congruency × hand, F (1, 22) < 1, p =.88).

2The remaining effects were site main effects (250(225-275) ms, 550 (525-575) ms, 600 (575-625), and 650(625-675) ms (all F -values > 6.9, all p-values < 0.006),whereas all remaining main and interaction effects fell be-low significance.

3All remaining main and interaction effects fell belowsignificance, with the exception of a region effect in the600 (575-626) ms bin, F (1, 23) = 7.8, p = 0.01.

4These results remained by and large identical whenthe ERPs were re-referenced to the average of TP9 andTP10.


K. Schneider – Neuroimaging in German Court Rooms

Abstract

K. Schneider (Aachen, Germany) – Neuroimaging in German Court RoomsSteiner (1981), an Austrian philosopher of the 20th century, stated that a deep understanding of human

life and nature should be the essential prerequisite for legislation and jurisdiction, and the foundation of

all legal studies. Neuroscience, claiming to give new insights into human nature, leads to an outstanding

current relevance of Steiner’s conclusion: By targeting fundamentals of the human self-conception (e. g.

free will), the rapidly growing field of cognitive neuroscience and neuroimaging in particular challenges

the traditional way of thinking in many sciences, the humanities, and the law. The use of neuroimaging

methods as evidence in legal proceedings is meanwhile a key part of scientific discussions, and also at-

tracts attention of the legal practice. However, ”lie detection”, the most popular aspect of neuroimaging in

court, is only one aspect of the possible legal/forensic applications of brain scans. Even more questionable

is the attempt of “diagnosing criminals”, thus the idea of revealing potentially dangerous behavior traits

by means of a brain scan. These intentions are not only ethically alarming, but also raise legal questions.

Though neuroscientific research will probably not completely change the fundamental principles of the

(German) law system, there is an urgent need for discussion with special regard to legal regulation. The

present paper is divided into two parts, of which the first one introduces neuroimaging studies on rele-

vant legal and forensic questions, while the second gives a legal commentary on the implications of this

research.

Keywords: Law and neuroscience, Neuroimaging, Lie detection, “Diagnosing criminals”

Neuroimaging in GermanCourt Rooms

Karla Schneider, Department of Psychiatry,Psychotherapy and Psychosomatics, IRTG 1328,

Pauwelsstr. 30, 52074 Aachen, [email protected]

Introduction

”Is it possible to diagnose pedophilia with thehelp of brain scans?” A German law officeposed this question to a researcher in the fieldof neuroscience at the beginning of 2008. Oneof their clients was found guilty of sexually

abusing two adolescent girls and sentenced toprison. However, the court’s decision was builton circumstantial evidence, and there was noclear proof for or against the offense. Hence,the lawyers, inspired by the media, were inter-ested in the possibilities given by the new neu-roscientific methods of brain scanning to havethe court procedure revisited.

This short episode reveals not only the prac-tical relevance of neuroscientific methods, inparticular of functional magnetic resonanceimaging (fMRI), but also the danger of thesetechniques as they are misleadingly thought toprovide objective measurements of guilt andcriminal behavior.



Developed for medical purposes to aid neu-rological diagnostic examinations, neuroimag-ing quickly attracted the interest of scientistsbecause of its social applications. If it is possi-ble to detect tumors and blood flow in the brainto diagnose pathological aberrations, why nottry to brain-read the thoughts of healthy peo-ple, criminal offenders in particular?

The present paper will be divided into twoparts: first introducing neuroscientific researchon relevant forensic questions, followed by alegal commentary on the implications of thisresearch.

The Neuroscientific Point of View

Introduction to neuroimaging

fMRI is the most popular neuroimaging tech-nology because according to today’s medicalknowledge, its use is harmless. It is non-invasive, as it uses the level of blood oxy-genation as a ”brain-internal” contrast medium(the so called BOLD contrast - Blood Oxy-genation Level-Dependent Contrast) (Jäncke2005). The magnetic field strength, that iscommonly used, is 1.5 or 3 Teslas.

The theory behind fMRI is that a workingneuron needs more oxygen than a neuron atits ”resting state”. When neurons are acti-vated, the level of oxygen in the brain regionwhere they are located immediately drops. Un-fortunately, today’s technology cannot mea-sure this ”initial dip” of oxygen, but only thesubsequent increase. For reasons that arenot fully understood, the brain overcompen-sates for the decreasing amount of oxygen be-fore it falls back to the null level of an inactiveneuron (Goebel & Kriegeskorte 2005). Thesechanges in blood-oxygen level lead to changes

in the electromagnetic signal that can then beregistered. This signal depends on the under-lying substance, e.g. different types of tissueand the liquor, and therefore allows analysesof brain structure and/or the activity of the brainduring a certain task.

While fMRI guarantees a relatively satisfy-ing spatial resolution, it suffers from a time lagdue to the fact that the increase of blood oxy-gen appears about two to three seconds af-ter the onset of neural activity. This lag maybe overcome by the use of multimodal imag-ing (e.g. one of the first trials by Gamer etal. 2007), i.e. by combining fMRI with an-other method such as electroencephalography(EEG), which is known to have poor spatial,but very good temporal resolution. Anotherconceivable possibility is combining polygra-phy with neuroimaging.

Further neuroimaging methods are PositronEmission Tomography (PET) and Near-Infrared-Spectroscopy (NIRS), but so farthese are rarely used in ”forensic functionalbrain imaging” (Langleben & Dattilio 2008).Their practical disadvantage is that the needfor nuclear tracers in PET and NIRS onlyallows for the study of activity relatively closeto the surface of the cortex and not of deeperstructures.

Research on ”neuroscience-based” liedetection

Simultaneously with the rejection of poly-graphic evidence In Germany by the ”Bundes-gerichtshof (BGH)” (German federal court) in1998 (BGHSt 44, 308) (see also below), theinterest of neuroscientists in neuroimaging-based ”brain reading” was increasing. KathyO’Craven and Nancy Kanwisher (O’Craven



& Kanwisher 2000), while investigating vi-sual stimuli and their neural correlates, wereamong the first who stated that the dream ofreading human thoughts might finally cometrue. From there, it did not take long before thefirst studies on detecting lies in the brain werepublished. Leading researchers in this field areDaniel D. Langleben (Langleben et al. 2005,2006) and Christos Davatzikos (Davatzikos etal. 2005), both professors at the University ofPennsylvania. Davatzikos is also the scientificcounselor for the commercial brain readingfirm, No Lie MRI (www.noliemri.com; see alsowww.cephoscorp.com).

To conduct polygraphic lie detection exami-nations, there are basically two ways of testingavailable: the so called Guilty Knowledge Test(GKT) and the Control Question Test (CQT).

The GKT provides a kind of ”multiple choice”test, which consists of several items as poten-tial answers to a given question (e.g. ”Thecolor of the shoes of the victim was a) blue,b) red, c) brown, d) black.”). The theorybehind the polygraphic GKT is, that the de-facto-offender would show increased reactions(namely electrodermal activity (EDA)) towardsthat stimulus, which pertains to the facts ofthe offense, while non-offenders would showthe same physiological response towards eachof the presented items. The problem withthis test is that it only makes sense in suchcases in which just the accused offender hascrime-related knowledge, and thus has a pre-requisite, which is hard to fulfill in times ofwidespread public media. Additionally, it re-mains unclear, whether a physiological re-sponse to a stimulus is really related to the of-fense or whether the item just evoked anothermemory, which is emotionally relevant to the

interview person.

The CQT, which is more rarely used, isbased on a set of questions, of whom two areoffense-related, two are somehow emotionallyrelevant and at best evoke an insecurity aboutthe correct answer (e.g. ”Did you ever steelsomething before the age of 18?”) and twoare emotionally irrelevant (e.g. ”Are you sit-ting on a chair?”). The participant is asked toanswer every question with ”No” (in rare caseswith ”Yes”), no matter whether ”No” is true orfalse. The idea behind this test as a poly-graphic examination is that someone who is fa-miliar with the details of the offense will showthe most pronounced reaction when denyingknowledge of the crime, as seen when an-swering the offense-related questions. How-ever, the CQT examination raised even moreconcerns than the GKT, as its questions haveto be generated conjointly with every individ-ual test person in every single case, whichmakes this method and its results very subjec-tive and hardly comprehensible to neuroscien-tific lay people, including judges.

The results of both, GKT and CQT, are ad-ditionally questioned for relying significantly onthe experience of the investigator. Aside fromthese two basic test variants there are somemodifications and supplements which are stillto some extent based on the principles of GKTand CQT.

The most widespread hypothesis behindneuroscientific lie detection studies is that alie would take up more cognitive resourcesthan telling the truth, since a lie would be acombination of inhibiting the true answer andcreating the lie. Studies in the field are mostlybased on polygraphic test concepts modeledafter the GKT. However, there are a few ex-



ceptions dealing with a form of the CQT (Kozelet al. 2005).

Many studies apply a comparable and sim-ple task, the denial of a playing card. In thestudy conducted by Langleben et al. (2005),participants received a $20 note and a play-ing card. During the scanner session, theywere presented a sequence of playing cardsand asked to deny the ownership of every pre-sented card, even if it was the one that theyhad been given previously. Increased activa-tion was found for the lie condition compared totruth condition, particularly in brain areas thatare also related to behavioral inhibition (e.g.anterior cingulate gyrus (ACC); Agam et al.2010; Hester et al. 2004). According to theauthors, this data supports the hypothesis of alying being a more complex cognitive act thantruth telling (Langleben et al. 2005).

A similar task was chosen by Davatzikos etal. (2005) who confirmed a stronger activa-tion of the ACC and lateral prefrontal areasfor the Lie > Truth contrast. To set up morerealistic scenarios, recent studies have usedmock crime situations, in which none of the in-vestigators, except a study coordinator, are in-formed about which of the participants is play-ing the role of the ”criminal” and which as thecontrol person (Kozel et al. 2009). ThoughKozel et al. (2009) could come up with a 100%sensitivity rate, the specificity of fMRI lie detec-tion was low (33%). Moreover, the high sen-sitivity was the result of extensive analyses,which also influenced the selection of the finalgroup of participants (see Table 1).

While most investigations choose to usefMRI for the detection of lies, there are a fewexceptions of those who use PET (Abe etal. 2006), EEG (”brain fingerprinting”, P300-

analysis, Mertens & Allen 2008) or NIRS (Tianet al. 2009), indicating a role for the lateral andmedial prefrontal regions and for the ACC indeception.

Mock crimes are an attempt to better ap-proximate reality. However, it is not only thecomplexity of the generated task, which needsto be discussed: Real-life settings displaymany grey areas between truth and lie andthus, it would be a key issue to find a way todistinguish between truth, conscious lies andfalse memories or related grey ”in-between” ar-eas.

Thus, investigating activation of real andfalse memories was the aim of Markowitschet al. (2000). According to their results, realmemories evoke stronger responses in the lim-bic system, the right amygdala in particular,and thus in emotion-related areas.

The criticisms, which were brought forwardagainst the use of ”forensic functional or struc-tural neuroimaging”, were and are still mani-fold and predominantly address methodologi-cal aspects. Though studies on lie detectionrevealed comparable networks, which seem tobe involved in the process of telling a lie, andcould partly come up with impressive sensi-tivity values up to 100% in case of the Kozelstudy (Kozel et al. 2009), they are still stan-dardized lab situations. Generating stimuli forthe use in a neuroimaging study and eval-uating the data require extensive analyses.More, the technology of the current methodswith their relatively poor spatial and/or tempo-ral resolution combined with the yet incompleteunderstanding of structure-function relations ofhigher cognitive functions in the human braindo not allow for making statements about themeaning of the brain activation of individuals,



Table 1: Examples of studies on lie detection

Study Method Participants Task ResultsMarkowitsch etal. 2000

fMRI Healthy volun-teers

Generating a reallife situation and acomparable falsestory and remem-bering both duringthe scanner session

Real Memories > FalseMemories. Stronger rightamygdala activation

Spence et al.2001


Lying about real lifesituations

Lie > Truth: Stronger activa-tion of ventro-lateral and an-terior cingulate regions

Langleben et al.2002


Denying ownershipof a playing card(variant of the GuiltyKnowledge Test)

Lie > Truth: Stronger activa-tion of left anterior cingulate,right superior frontal gyrus,prefrontal to dorsal premotorcortex, anterior parietal cor-tex and inferior intraparietalsulcus

Langleben et al.2005



Lie > Truth: Stronger activa-tion of the parietal cortex, in-sula, medial and lateral pre-frontal cortex, anterior cin-gulate cortex

Davatzikos etal. 2005



Lie > Truth: Stronger activa-tion of the parietal cortex, in-sula, medial and lateral pre-frontal cortex, anterior cin-gulate cortex

Abe et al. 2006 PET Healthy volun-teers

Telling the truth andlying about experi-enced and unexpe-rienced events

Lie: Lateral and medial pre-frontal cortex; Pretendingnot to know: ACC

Gamer et al.2007

fMRI andpolygraphy

Healthy volun-teers


Lie > Truth: Stronger activa-tion of the cerebellum, rightinferior frontal cortex, infe-rior motor cortex

Mertens & Allen2008

EEG Healthy volun-teers

Virtual reality crimescenario

Tian et al. 2009 NIRS Healthy volun-teers

Mock crime Lie > Truth: PFC

Kozel et al.2009


Mock crime (variantof the Control Ques-tion Test)

Lie > Truth: Stronger acti-vation of orbitofrontal cortex,dorsolateral cortex, anteriorcingulate cortex



especially not in real-life settings. Additionally,the identified regions (e.g. ACC) are not func-tionally and/or structurally specific to the act ofa lie, as they are also associated with work-ing memory (e.g. Broome et al. 2010), self-concept (e.g. Rameson et al. 2010) and fur-ther higher cognitive abilities. Also, regions asthe ACC and amygdala consist of structurallyand functionally differing subunits, an often un-derestimated aspect. With the help of fMRIand the other common methods of neuroimag-ing, it is currently not possible to exactly deter-mine, which part of a certain brain region playsa role in which task (Axer et al. 2010).

More, the groups of participants in the stud-ies are usually small (around 20 per study, onlynine in the final sensitivity analysis of the Kozelstudy, Kozel et al. 2009) and at the sametime very homogeneous comprising of healthyCaucasian students in their twenties with anabove average IQ, who join the studies volun-tarily. But these samples are far away from theforensic reality (Schneider et al. 2006), wherethe mean levels of education and IQ are sig-nificantly below these participant samples andalso the variety of age and ethnicity is muchbroader. While the understanding of the brainand neuroimaging technologies is still in its in-fancies, there is even more a lack of knowl-edge to which extent these factors might influ-ence the results of a brain scan.

”Diagnosing Criminals”

While the interest in neuroscience-based liedetection has decreased slightly in the pasttwo to three years, there has been a growinginterest in analyzing brain structure and func-tion of criminal offenders and paraphiliacs, andin the neural correlates underlying moral be-

havior (Greene 2006) (for an overview of cur-rent studies see Tables 2 and 3).

The idea of linking physical traits to crimi-nal or moral/immoral behavior traits is not new.In the mid 19th century, Cesare Lombroso,an Italian physician and psychiatrist often re-garded as the ”father” of criminology, alongwith his student Raffaele Garofalo and the fol-lowers of phrenology tried to link certain phys-ical traits to criminal behavior. While Lom-broso was mainly interested in the shape of theface, the idea behind phrenology was to ana-lyze bumps on the skull: special areas of thebrain were assumed to be responsible for cer-tain behavioral traits. If a bump over an areawas found, this area and its function were saidto be pronounced (Meier 2006) and would po-tentially indicate a certain aspect or character.

Modern desires to investigate the brains ofpsychopaths or other criminal offenders havebeen criticized as a revival of these ideas andhave been referred to as ”modern Lombro-sionism” (Tondorf 2008; Baskin et al. 2007)or ”modern phrenology”. Though it is notcontroversial that certain brain structures arededicated to certain brain functions such asBroca’s Area for language processing, exactlylocating higher cognitive functions is currentlyimpossible due to the exceeding individualvariability of brain shapes, insufficient accu-racy of contemporary methods and because ofconceptual ambiguities. Only a few studies arediscussing issues of the use of complex termsas ”lie” (Langleben et al. 2005) or ”morality”(Moll et al. 2002) and likewise, there is no stan-dardized diagnosis of psychopathy. The lack ofclear definitions of what to investigate makesthe results of studies questionable and hardlycomparable across studies (Bennet & Hacker



Table 2: Study examples on neuroscience and criminal behavior.

Study Methods Group ResultsCriminals/ Psy-chopathy andrelated topicsSoderstrom etal. 2000

SPECT Non-psychoticviolent offend-ers

Reduced regional cerebral blood flow (rCBF) in the right an-gular gyrus, in the right medial temporal gyrus, bilateral hip-pocampus and left frontal white matterIncreased rCBF in the parietal associative cortex bilaterally

Lindberg et al.2005

EEG Murderer withantisocialpersonalitydisorder

Reduced alpha-, but bilaterally increased theta- and delta-waves in arousal EEG, in occipital regions in particular. Al-tered brain maturation? Altered day arousal

Deeley et al.2006

fMRI Psychopathiccriminal offend-ers (PCL-R-Score > 25)

Reduced and even increasing activation of the fusiform facearea and extrastriatal cortex during viewing of (fearful) facialstimuli

Schiltz et al.2007

fMRI Pedophiles Reduced right-sided amygdala volume. Reduced white mat-ter in the right amygdala, the hippocampus bilaterally, septalregions and the substantia innominata. Increase of the righttemporal pole

Anckarsäter etal. 2007

SPECT Violent offend-ers

Frontotemporal hypoactivation

Müller et al.2008

StructuralMRI

Psychopathiccriminal offend-ers (PCL-Rscore > 28)

Increase of gray matter in frontal and temporal regions, in theright superior temporal gyrus in particular

Tiihonen et al.2008

MRI (Voxel-based mor-phometry)

Criminal offend-ers with antiso-cial personalitydisorder (PCL-R score > 30)

Atrophic gray matter in the postcentral gyrus, frontopolar andorbitofrontal cortex, which was positively correlated with thePCL-R score. Increased white matter in the right cerebellum.Bilaterally increased white matter in the occipital and parietallobe and in the left cerebellum. Within the offender groupno correlation between increased gray and white matter andthe PCL scores, substance abuse, the use of psychotropicpharmaceuticals and global IQ



Table 3: Study examples on neuroscience and criminal behavior.

Study Methods Group ResultsMoral BrainMoll et al.2001 fMRI Healthy partici-

pantsMoral > Morally Irrelevant: Fronto-polar cortex, medial frontalgyrus, right anterior temporal cortex, lenticular nucleus, cere-bellum

Moll et al.2002 fMRI Healthy partici-pants

Moral judgments: Medial orbitofrontal cortex, temporal pole,STS. Emotional, but non-moral judgments: Left amygdala,lingual gyri, lateral orbital gyrus

de Oliveira-Souza et al.2008

StructuralMRI

Psychopaths(PCL:SV-Score17.8 3.8)

Decreased gray matter in the prefrontal cortex, orbito-frontalcortex (laterally and left medial), superior temporal sulcus,medial anterior insula and left anterior temporal cortex. Sig-nificant correlation between reduced gray matter and antiso-cial behavior

2003).

Most of the forensic studies refer to indi-viduals with antisocial personality disorder oreven psychopathic traits, which is a commongroup among convicted felons. (Schneider etal. 2006). The studies reveal alterations anddysfunctions of prefrontal and parietal regionsand parts of the limbic system such as theamygdala (see Weber et al. 2008 for review).

Another focus is shedding light on the neu-ral correlates of the basic ability to distinguishbetween right and wrong. Moll, de Oliveira-Souza and colleagues began investigating theneural substrates of moral decision making inhealthy people (Moll et al. 2001). They fol-lowed up with structural MRI studies on psy-chopathic brains, concluding that there are dis-tinctive deviances in regions that are associ-ated with morally-desirable behavior, in par-ticular the ventro-medial prefrontal areas (deOliveira-Souza et al. 2008).

While moral studies reveal a functionalnetwork of certain brain areas including theventro-medial prefrontal cortex, the anterior

cingulate and posterior cingulate cortex, pari-etal areas and the precuneus, these regionsare not specific to moral reasoning and alsofound in studies concerning self-referentialcognition (Rameson et al. 2010) and theresting state (Mason et al. 2007). Addition-ally, studies on moral decision making mostlylack a clear definition of the term ”morality”(Bennett & Hacker 2003).

The Legal Point of View

History of Lie Detection in Germany

Lie detection is, and always has been, atbest, skeptically considered in German ju-risdiction. However, the ”Bundesgerichtshof(BGH)” (German federal court) and the ”Bun-desverfassungsgericht (BVerfG)” (Germanconstitutional court) have three pertinent de-cisions regarding the validity of lie detectorscurrently in court.

In 1954, the BGH (BGHSt 5, 332) inter-preted the use of polygraphic lie detection asan offense against human dignity (Art. 1 I



”German Grundgesetz” - GG). Polygraphy wasregarded as an illegal intrusion into the sub-conscious mind. In 1981, the BVerfG (BVerfGNStZ 1981, 446) still agreed with the ruling ofit being an offense against the principles offundamental law - though not against humandignity but against personal rights (Art. 2 I,1 I GG) - in 1998, the BGH (BGHSt 44, 308)denied any transgression of fundamental legalprinciples. However, polygraphy was not ac-cepted as legal evidence either. On the con-trary, after reviewing four expert reports theBGH stated the infeasibility of the use of thepolygraphic lie detector in court. As a result,even today the lie detector has not made itsway into the German law system.

Discussing Neuroscience

As pointed out by the BGH in 1954 (BGHSt 5,332), the use of polygraphs as lie detectors incourtrooms may only be justified following therules of law and not primarily by scientific evi-dence. Emanating from that, during that deci-sion the BGH analyzes the meaning of polyg-raphy according to the legal guideline of hu-man dignity.

Like polygraphy or forensic DNA analysis,neuroscience challenges fundamental princi-ples of law such as human dignity, rights ofpersonality and principles of the law of evi-dence (Spranger 2009, Beck 2007). Its inpart intrusive methods require detailed discus-sions on potential applications and the needfor regulations. Likewise the BGH in 1954for the polygraphy with regard to neuroscienceSchauer (2010) points to the questionable con-fusion of normative terms as guilt and respon-sibility and descriptive standards of statisticsand psychological evaluations: What works

for science needs not work for law and viceversa, as both disciplines are following differ-ing standards. Thus, the decision about ad-missibility of evidence in courtrooms must notonly be based on scientific principles such asstatistical values and the construct validity ofparadigms, but also has to take legal stan-dards into account. More even, to avoid a kindof ”neural fallacy” one has to consider that it isoutside of the function of a descriptive sciencesuch as neuroscience to determine whetherthe prerequisites of the criteria of law princi-ples are fulfilled. In order to ensure a reason-able way of dealing with the new neuroimag-ing methods one has to thoroughly pay atten-tion to which (legal) goals can be addressedby scientific studies and to consider what canbe derived from their results (Brown & Murphy2010; Greely & Illes 2007).

Conclusion

Though there are some promising and impres-sive developments in the field of neuroscience(Axer et al. 2010; Kozel et al. 2009; Hayneset al. 2007), the current neuroimaging technol-ogy does not allow for conclusions about thehigher cognitive functions of a single personin a way that makes it suitable as evidencein court (Spranger 2009; Beck 2006). How-ever, the rapidly growing technology exposesthe need for regulations in order to guarantee astandardized handling of neuroimaging and athorough consideration of its impacts for soci-ety, also taking its potential suggestive effectsinto account (McCabe & Castel 2008). To al-low for exact definitions of research objectivesand the implications of the results, an intensi-fied discussion between lawyers and neurosci-entists is highly desirable.



Acknowledgements

The project was supported by the Andrea-von-Braun-Stiftung and written during funding bythe German Research Foundation (”DeutscheForschungsgemeinschaft, DFG”, IRTG 1328).

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T. Sauer – Time-Frequency Analysis, Wavelets and Why Things (Can) Go Wrong

Abstract

T. Sauer (Giessen, Germany – Time-Frequency Analysis, Wavelets and Why Things (Can) GoWrongWavelets are an increasingly popular tool in time–frequency–analysis that helps, among others, to detect

time localized frequency components in a signal. Because of that, they are frequently used in the analysis

of biosignals or of technical systems. However, the underlying mathematical theory that makes things

work so beautifully is based on some nontrivial assumptions whose violation makes the tool useless and

creates information that leads to misinterpretation of the signal content. This article gives a brief overview

over the background of the wavelet transform in continuous theory and digital practice and highlights

some of the difficulties that can arise if the transform are applied inappropriately.

Keywords: Wavelets, Fourier transform, Gabor transform, numerical computations

Time-Frequency Analysis,Wavelets and Why Things

(Can) Go Wrong

Tomas Sauer, Lehrstuhl für NumerischeMathematik, JLU Giessen,

Heinrich–Buff–Ring 44, D–35392 Gießen,Germany

[email protected]

Introduction

Nowadays, the wavelet transform has becomequite a standard tool for time–frequency anal-ysis that allows for signal processing in termsof resolution of time and frequency.

There is a simple musical analogy that helpsus to understand the meaning of that sen-tence. The classical and well–known Fourier

transform decomposes a signal into its fre-quency components and is ideally suited forthe analysis of a single tone played by a mu-sical instrument where the tone is rewritten asa superposition of its partial tones which, in ourmusic analogy, appear with frequencies thatare multiples of the frequency of the tone it-self, (Helmholtz, 1885). The spectrum givesus information on the nature and “color” of thetone but it lacks any time information. Thismakes perfect sense as the tone is a periodicfunction and any time information only affectsthe phase of the signal which is mostly irrel-evant. The situation changes as soon as, in-stead of a single tone, a melody is considered,that is, a sequence of different tones of differ-ent duration. Perceiving the melody is a taskwhere the Fourier transform fails completely:all that it is able to figure out is which tone hadcontributed which percentage to the melody.Though this may be statistically interesting, it



Figure 1: The spectrum (above) and the “wavelet

scalogram” (below) of the three tones and the

chord.

gives no information about the melody. This isthe point where time–frequency analysis en-ters the scene, trying to figure out whethersome frequencies or frequency componentsappear locally in time. Let us rush ahead a bitand consider a very simple example where apure sine is played, followed by its pure thirdand fifth and, finally, the full chord. As canbe seen in Figure 1 the spectrum is a purely“statistical” evaluation of the frequencies thatoccur in the course of the “melody” while thescalogram shows the “melody” in some almostmusical notation. Note, however, that real-ity would not be that simple as practically anyrealistic signal is composed of various partial

Figure 2: A snippet from some real musical record-

ing. The appearance of overtones makes things

a lot more complicated even if some piece of the

melody could be guessed.

tones and not a pure sine as here. Look atFigure 2 for a small example. We will return toFigure 1 several times in this paper as the twopictures show even more effects that typicallyappear in numerical signal processing.

The idea of time–frequency precedes thatof wavelets, the windowed Fourier transformbeing the oldest and most straightforward ap-proach, followed, for example, by the Gabortransform, cf. (Gabor, 1946). A good sourceof information in width and depth about time–frequency analysis is the excellent book byMallat (Mallat, 1999), a very easygoing intro-duction on a journalist level can be found in(Hubbard, 1996).

In general, no perfect localization in time andfrequency is possible as is stated in the famousHeisenberg uncertainty principle. Again, wecan express this in a musical analogy: it is im-possible to play a jig on the bass pedals of anorgan, no matter how fast your feet are. To ex-plain and understand this effect, just keep inmind that in order to be audible a tone should



have at least one oscillation which takes a timethat is reciprocal to its frequency. If the toneis played in more rapid sequence than thistime permits, it is not the tone any more, itneeds partial tones of much higher frequencyto obtain the “truncation” effect. Hence, itsbetter localization in time (the rapid playing)destroys its localization if frequency (the puretone). Why this is mentioned? It has the sim-ple but fundamental consequence that there isno perfect version of time–frequency analysisand therefore any attempt to perform such adetection of time local frequency componentsmust have its advantages and drawbacks thatrequire choosing and, if necessary, adaptingthe method to a specific task. This paper willfocus on the wavelet transform and how it canbe used as a time localized bandpass filter,i.e., how to localize certain frequency com-ponents in time and then remove them fromthe signal. This requires an analysis step thattransforms the signal into it scalogram, somesort of time dependent spectrum, and a syn-thesis step which reconstructs the original sig-nal from the possibly modified scalogram. Allthis is, by nature, mathematical and any rea-sonable and understandable presentation ofthe material requests an appropriate amountof formulas and formalism. I will try to be asprecise as possible, but will always sacrificedetails (as important and crucial as they maybe) for the sake of explaining the ideas andconcepts.

There is also a discrete wavelet transforma-tion, based on the concepts of multiresolutionanalysis (MRA) and filterbanks, cf. (Cavaretta,Dahmen, & Micchelli, 1991; Daubechies,1992; Mallat, 1999; Strang & Nguyen, 1996;Vetterli & Kovacevic, 1995). This is wonderful

theory with plenty of applications, for examplein the JPEG2000 standard, but this is notwhat we are interested in here. This paperdeals with discrete aspects of the continuouswavelet transform that result from the verysimple fact that all numerical computations areof a discrete nature.

Basics

In this section, we will review some of the ba-sics of Fourier transform and time–frequencyanalysis, aiming not so much for complete-ness or details and definitely not for proofs ofthese concepts, but for the hidden catches inthe mathematics that often are missing in en-gineering or biosignal processing literature.

In most of signal processing, signals aremodeled as real valued L2–functions, that is,functions f whose energy integral

‖f‖2 :=

∫R|f(t)|2 dt (1)

is finite. In fact, this finiteness of the energynorm ‖ · ‖2 is what defines a square integrableor L2–function. With the hair–splitting preci-sion mathematicians are often accused of, ithas to be mentioned that this is an integral inthe Lebesgue sense (thus the letter “L”) andthat such function are not really pointwise ob-jects as they can be altered on a set of mea-sure zero. All definitions and basic propertiescan be found in any reasonable book on anal-ysis, with analysis to be understood in somecontrast to good old calculus. Fortunately, thesubtle points to be taken care of in Lebesgueintegrals do not really matter – at least usually.Keep in mind, however, that very simple ob-jects like constants, polynomials or oscillationslike sine and cosine do not belong to the classL2.



The use of the letter “t” in (1) already indi-cates what type of signals we have in mind,namely real valued time series like musicrecordings or biosignals like the channels ofan EEG. All these realistic signals are finite– not finite, however, because of their nature,but because we only record and analyze finitechunks of data from a larger context: neitherdoes the brain activity of the test person endwith the experiment, at least not always, nor isthe studio turned into eternal silence once therecording of a piece of music is finished. The-oretically, finite signals are great as for suchsignals the only way to reach infinite energyis the very unrealistic case of a singularity oc-curring, but since our signals are not finite bynature, only finite by measurement, we haveto be prepared to face unwanted artifacts.

Fourier and windows

The Fourier transform of a signal will be de-fined here as

f(ξ) =

∫Rf(t) e−iξt dt, ξ ∈ R.

The function f is called the spectrum of thefunction f , contains essentially the same en-ergy,

∥∥∥f∥∥∥2

=√

2π ‖f‖2 (the factor√

2π isdue to an ubiquitous normalization issue of theFourier transform which can and usually willcause serious trouble in careless applicationsof software libraries) and provides full informa-tion about f as there exists the inversion for-mula

f = f∨, g∨(t) :=1

2π

∫Rg(ξ) eiξt dξ. (2)

So all is well that ends well? No, not really.Mathematics are usually correct, but they areonly correct within a certain framework that

has to be understood and interpreted properly!All the above results are L2–statements andonly hold true in the “world” of L2 functions.Particularly that means:

1. Equation (2) does not hold true in point-wise sense, it can be violated on a setof measure zero which may even includeall points where the integral can really becomputed – explicitly or numerically.

2. The theory already excludes a lot of “in-teresting” functions like constants (whichusually do not even have a Fourier trans-form) or periodic functions. In fact, eventhe Fourier transform for signals of finiteenergy is even more tricky as it is obtainedby a completion argument and not directly.

3. Periodic functions have to be handled bymeans of Fourier series which are trigono-metric polynomials and their associatedspectrum is not a function defined on thecontinuum R but a sequence defined onthe integers Z. There is a whole the-ory of such groups and dual groups, thebasis of modern Harmonic Analysis, anice introduction to which can be found in(Katznelson, 1976).

4. Things are significantly easier whenfinitely supported signals are considered,and after all any opera starts and endssometime (but first the fat lady has tosing). Nevertheless, usually these finitesignals will eventually be embedded intosignals defined on all of R, as handlingfixed beginning and end also createsdifficulties.

The Fourier transform computes “only”, or,more euphemistically, “precisely”, the fre-quency content of the signal, and the complex



number f(ξ) describes the amplitude and thephase of the respective frequency contentsimultaneously.

The simplest way to pass from the Fouriertransform to some elementary form of time–frequency analysis is by means of windowing.Instead for transforming the entire function f ,the spectrum is computed only for a part of it.This task can be performed, for example, byconvolving f with a window function w whosecompact support (the region where the func-tion is nonzero) is centered around the origin.The latter is by no means necessary for thetheory to work, but coincides better with thegeneral intuition. The windowed part of f isthen obtained by multiplying f with a u–shiftedwindow,

fw,u(t) = f(t)w (t− u) ,

simply “cutting off” all information on f out-side the window. If, for example, w “lives” onlyon [−1, 1], then fw,x considers only the valuesf(t) for t ∈ [x − 1, x + 1], which is the windowaround t. The Fourier transform of the win-dowed function, also known as the short timeFourier transform, is

fw,x(ξ) = (f(·)w (·+ t))∧

(ξ) (3)

= f(ξ) ∗(eiξ·w

)(ξ) (4)

with the convolution

(f ∗ g) (t) :=

∫Rf(s) g(t− s) ds.

In terms of signal processing, convolutions areoften identified with filtering, cf. (Hamming,1989), so that this again is a well known op-eration: the spectrum (not the signal itself!)is filtered by a modulated and phase shiftedFourier transform of the window function w.This operation does not come for free as it

introduces windowing artifacts, known as theleaking effect, see again (Hamming, 1989),that lead to a “distorted” spectrum that has tobe interpreted with care.

But back to (3). This formula defines theshort time Fourier transform of f around x as

f (x, ξ) := (f(·)w(· − x))∧

(ξ) (5)

and has two parameters, x, ξ ∈ R, corre-sponding to the “positions” x in time and ξ

in frequency. Back to our musical analogy,the short time Fourier transform computes thespectrum, i.e., the frequency content over alimited time of our musical record, maybe a baror a single tone, depending on the size of thewindow. It should be clear that this window hasto be small enough to distinguish between dif-ferent tone and that we will not get a preciseresolution of frequency whenever the windowcovers the transition between two tones.

Time, frequency, and Heisenberg

In time–frequency analysis we consider amore general analysis tool, namely an inte-gral by means of so called time–frequencyatoms φu,ξ, indexed by time parameter u anda frequency parameter ξ. Formally,

Tφf (u, ξ) =

∫Rf(t)φu,ξ(t) dt. (6)

In the example of our short time Fourier trans-form, also referred to as Gabor transform,the time–frequency atoms were the modulatedwindow functions

φu,ξ(t) = e−iξt w (t− u) , (7)

where the window w is a real–valued symmet-ric funtion, i.e. w(t) = w(−t), and the e−iξt

term is responsible for the close relationship to



the Fourier transform. The Fourier transformitself is given in the context of time–frequencyatoms by

φu,ξ(t) = e−iξt, i.e., w ≡ 1,

and thus simply ignores the time component u.After all, Fourier analysis is frequency analysisin its purest form. An obvious advantage of theGabor transform or of any type of windowedFourier transform is that the frequency part ofthe transformation is really a frequency andnot some parameter somehow related to fre-quency as the scale parameter in the wavelettransform will be; this can become a very im-portant point, for example in audio applica-tions.

A fundamental property of a time–frequencyatom is its ability to localize the information intime and frequency. To quantify this and toclarify what we are actually talking about, wedefine the localization of a function f in timeand frequency as

µ(f) :=1

‖f‖22

∫Rt |f(t)|2 dt (8)

µ(f) :=1

2π‖f‖22

∫Rξ∣∣∣f(ξ)

∣∣∣2 dξ, (9)

and the associated variations as

σ2(f) :=1

‖f‖22

∫R

(t− µ(f))2 |f(t)|2 dt,

σ2(f) :=1

2π‖f‖22

∫R

(ξ − µ(f))2∣∣∣f(ξ)

∣∣∣2 dξ.The idea behind the concept of localization ismore intuitive than it may seem from equation(8): if, for example, f “lives” only on the interval[t− ε, t+ ε] for some ε > 0, then |µ(f)− t| ≤ ε,i.e., µ(f) ∼ t and σ(f) ≤ ε. Therefore, we saythat f is perfectly localized in time if σ(f) = 0

and perfectly localized in frequency if σ(f) =

0. Unfortunately there is no perfect localization

as the Heisenberg uncertainty principle statesthat

σ2(f) σ2(f) ≥ 1

4(10)

for any function f so that the simultaneous lo-calization in time and frequency always hitsa lower bound. The “Heisenberg optimal”functions are the particular short time Fourieratoms

φ(t) = a e−iξt eb(t−u)2

, (11)

with the window functions eb(t−u)2

and the “tun-ing parameters” a, b ∈ C, ξ, u ∈ R. These win-dows are no more finitely supported but decayexponentially for t → ∞ provided that b liesin the left half plane, which is perfectly OK intheoretical terms but requires some care if thefunction is considered numerically and has tobe truncated in order to have finite computa-tions.

The time–frequency localization of a func-tion f or an atom φ can be visualized by theHeisenberg boxes

H(f) = [µ(f)− σ(f), µ(f) + σ(f)]

× [µ(f)− σ(f), µ(f) + σ(f)]

in the time–frequency plane R2 3 (t, ξ). Iff = φu,ξ is a time–frequency atom, we simplywrite H (u, ξ). The Heisenberg boxes for theGabor atoms (7), for example, are usually rect-angles around (u, ξ) with sides σ(w) and σ(w).It should be intuitively clear that the time–frequency resolution of time–frequency atomsis related to the area of the Heisenberg boxesand that a system φu,ξ : (u, ξ) ∈ Γ can cap-ture the time frequency content of an analyzedfunction f only if the associated Heisenbergboxes cover the time–frequency region of in-terest and the more these boxes overlap, thehigher the redundancy between the atoms will



be. Here the index set Γ can be R2 or an in-finite or finite subset of R2 – in practical ap-plications it will definitely be the latter. If weknow all values of the Gabor transform of afunction f , we can even reconstruct this func-tion by means of the “averaged inverse Fouriertransform”

1

2π ‖w‖22

∫R

∫Rf(u, ξ) eiξtw (t− u) dξ du. (12)

Again, this identity only holds true in the weaksense of L2 functions and not necessarily forany t ∈ R. Nevertheless, the existence of in-verse transforms fulfills an important purpose:it shows that the transform, in this case theGabor transform preserves all the informationabout the underlying function since the func-tion can be reconstructed from the values ofthe transformation. Whether the the functioncan be reconstructed from a discrete or evenfinite subset of transformation values and howsuch a subset should be constructed, is an-other issue.

Wavelets

Another family of time–frequency transformsis given by the wavelet transform. Here theatoms ψu,s, u, s ∈ R, are of the form

φu,s(t) :=1√sψ

(t− us

), (13)

where the function ψ is called the wavelet andthe word “frequency” has to be understood ina more generous sense as 1/u for the scaleparameter u. To be precise, 1/u is not the fre-quency, but related to it. The wavelet transformof a function f is defined as

Wψf(u, s) :=

∫Rf(t)

1√sψ

(t− us

)dt. (14)

f

t

Figure 3: The Heisenberg boxes of a wavelet; this

is, of course, only schematic, but at least the area

of the boxes is all the same as it should be.

The time–frequency boxes for wavelets

H(u, s) = [u− s σ(ψ), u+ s σ(ψ)]

×[µ(ψ)

s− σ(ψ)

s,µ(ψ)

s+σ(ψ)

s

]are of a different type than those above as theychange their shape according to the scale pa-rameter s. If s increases, that is, if the “fre-quency” 1/s is lowered, the box stretches intime direction and narrows is “frequency” di-rection, indicating an improved frequency res-olution for the price of reduced time resolu-tion, see Figure 3. In our musical analogy, alow tone takes some time to sound (it shouldat least perform one full period to be perceiv-able as a tone, which is a periodic event),hence cannot be located very well in time andtherefore precise measurements are not nec-essary. Instead, the wavelet has a good ca-pacity to discriminate between different fre-quencies there. After all, the low tones aredenser in frequency than the high ones.

Things turn around if s decreases: in “highfrequencies” the discrimination between fre-quencies deteriorates (what remains constantis the relative error in determining them) but



Figure 4: Zoom into the wavelet transform of the

“chord” signal

the time resolution improves. In summary onecould say:

The Gabor transform focuses on ab-solute precision in the localization oftime and frequency while the wavelettransform cares for relative precision.

Funny enough, the area of the Heisenbergboxes remains constant in both cases, it is4σ2(w) σ2(w) in the case of the Gabor trans-form and 4σ2(ψ)σ2(ψ) in the case of wavelets;both values have to be at least 1 by means of(10).

This effect of “relative precision” can actuallybe seen in our simple example of Figure 1. Ifone carefully looks at the chord on the righthand side of the image, there is a blur be-tween the two “high” frequencies while the twolower parts of the chord are better separated.Figure 4 shows a “zoom” to this effect and in-deed it should become even clearer that thereis this blur or leakage between the “frequencybands”. This is due to the decay of frequencyresolution for higher scales, and in order toavoid artifacts or, even worse, misinterpreta-tions of signals, it is of extreme importance to

carefully choose the frequencies or scales forwhich the wavelet transform is computed. Thiscan also mean to “trim” or “tune” the waveletsuch that it provides sufficient frequency res-olution in the “band of interest”. In terms ofHeisenberg boxes this means that the wavelethas to provide “sufficiently flat” boxes.

Also wavelets admit an inversion formula,namely

f = MψWψf (15)

with the “inversion formula”

1

Cψ

∫R

∫Rg(u, s)

1√sψ

(t− us

)du

ds

s2. (16)

We denote this expression by Mψg and thusobtain the inversion operator which is definedfor functions g of two variables, but obviouslythe existence of the double integral is again anissue by itself.

It is illustrative to look at the proof as some ofthe formulas and ideas will become importantlater. If we fix the scale s and consider thewavelet transform as a function in u, we canfollow a good engineering tradition and take itsFourier transform which yields

(Wψf(·, s))∧ (ξ) =√s f(ξ) ψ (sξ) . (17)

In the proof, one takes the u–integral from (16),uses the classical Perceval identity∫

Rf(t)g(t) dt =

1

2π

∫Rf(ξ)g(ξ) dξ

and substitutes (17). Applying the s–integral toall that stuff and doing a few relatively simplemanipulations like change of variables, we canexpress the double integral as a product of aninverse Fourier transform of f and the integral

∫R

∣∣∣ψ∣∣∣2|ξ|

dξ =: Cψ, (18)



which determines the value of the “magic” con-stant Cψ in (15) and completes the proof. Didwe forget something? Indeed! In order tohave a well–defined expression, the constantshould be finite, which is the famous admis-sibility condition for wavelets. Sometimes afunction is even called a wavelet only if the ex-pression in (18) is finite – which makes perfectsense as any function of that type must satisfy∫ψ = 0, that is, it has the same amount of

“mass” above and below the x–axis, which is a“wave–like” behavior. Again it is time for a fewremarks:

1. The wavelet transform (14) can be com-puted even if the underlying wavelet isnot admissible, in other words, even if thewavelet is not a wavelet. In fact, one ofthe most popular wavelets, the so–calledMorlet wavelet, see (Mallat, 1999) is notadmissible but nevertheless used for anal-ysis purposes.

2. If the wavelet is admissible, then thewavelet transform captures the full infor-mation on the function; after all, that iswhat invertibility of the transform means.However, an admissible wavelet always“kills” constants so that constants canalways be lost during a wavelet transform.This is perfectly in accordance with the“laws” of L2 as the only square integrableconstant function is the zero function. Inpractical applications, however, only afinite piece of the function is transformedand there shifts by constants could verywell matter – at least in part.

3. In general, modification by constants ofa finitely supported function only affectthat part of the wavelet transform where

the overlap between the constant func-tion and the wavelet takes place only ina non-relevant part of the wavelet. Inother words, such effects only show on theboundary of the wavelet transform.

Even if wavelets can be almost completely“custom designed” with the only requirementbeing the very mild admissibility condition (18),there are only three “classical” wavelets thatcover most of the known applications:

The Haar wavelet is the simplest case of awavelet and defined as

ψ(t) =

1, t ∈ [−1, 0),

−1, t ∈ (0, 1],

0, otherwise,

(19)

hence, it is compactly supported. It pro-vides excellent time localization but sinceits Fourier transform is the difference oftwo modulated copies of the function ξ :=sinπξπξ , the Fourier transform decays very

slowly leading to quite poor frequency lo-calization.

The Mexican hat wavelet is defined as

ψ(t) =(1− t2

)e−t

2/2 = − d2

dt2e−t

2/2

(20)and decays exponentially for |t| → ∞,which means still very good time localiza-tion even if the function is no more com-pactly supported. It almost coincides withits Fourier transform ψ(ξ) = ξ e−ξ

2/2 andtherefore offers good time and frequencylocalization.

The Morlet wavelet or “Morlet’s Gaussianwavelet” is the “complex brother” of theMexican hat and uses a complex modula-



tion of the form

ψ(t) = eiaωte−bt2/2, ω, a, b ∈ R+,

(21)instead of the polynomial component.Strictly speaking, the definition from (21)does not even satisfy the admissibilitycondition, but this can be easily solvedby adding a suitable correction term, cf.(Mallat, 1999). The decay parametersa, b allows to “tune” the wavelet to a cer-tain central frequency, cf. (Mallat, 1999).Loosely speaking, this means, we canuse it to determine the frequency or scalerange where the Heisenberg boxes areapproximately squares, where time arefrequency are resolved equally well.

Mexican hat and Morlet wavelet are not somemiraculous inventions of pure genius’ inspira-tion. Instead, they result from almost sys-tematic constructions of wavelets emerging ofthe time–frequency optimal frequency atomsin (11) which admit equality in the Heisenberguncertainty equation (10). Also the “differentia-tion trick” that leads to the Mexican hat waveletis based on a very simple idea: by means ofpartial integration it is very easy to see that∫

Rf(t)ψ(t) dt = 0

if f is a linear function of the form f(t) = at+b.The technical term for that property is to saythat ψ has two vanishing moments – one van-ishing moment would mean

∫ψ = 0, so the

Mexican hat “over-satisfies” this requirementby another polynomial, f(t) = t. In general,the wavelet is said to have n vanishing mo-ments if it “kills” all polynomials of degree < n,that is, if∫

Rtk ψ(t) dt = 0, k = 0, . . . , n− 1. (22)

Vanishing moments are crucial for the goodapproximation of smooth functions (functionsthat have a lot of derivatives) and for the de-tection of jumps and discontinuities. In fact,we now know how to construct wavelets withan arbitrary number of vanishing moments,namely, as derivatives of a function φ that hasto satisfy some mild conditions: ψ = dk

dtkφ au-

tomatically has k vanishing moments.

Customizing wavelets

One great advantage of wavelets is that thecan be customized to a given application.Since the wavelet transform (14) essentialllymeasures the correlation between the sig-nal and shifted and dilated (i.e., “frequencymodulated”) versions of the wavelet function,wavelet coefficients will be particularly largein modulus whenever the signal contains astrong “wavelet–like” piece. This can be madeuse of, for example in the analysis of EEGdata where often the detection of spindle–likefeatures is desired. But how to design?

The simplest way is to choose a function φ

such that ∫R

|φ(t)|2

|t|<∞

and to use φ as the Fourier transform ψ of thewavelet. We will see later when we considerthe numerical realization that this is perfectlysufficient, that indeed the wavelet itself will noteven be needed for a fast computation of thetransform. The disadvantage is that it is not soeasy to control the shape of the wavelet just bymeans of its Fourier transform.

A slightly more sophisticated approach is toadapt ψ as a linear combination

ψ =

N∑j=1

aj ψj , aj ∈ C, ψj ∈ Ψ,



where the wavelets ψj are chosen from a (pos-sibly infinite) dictionary Ψ of wavelet functionsor as scaled versions of the original wavelet.Under some mild conditions on Ψ the admissi-bility of the resulting wavelet function ψ can beeasily assured. The coefficients aj can then bedetermined by “tuning” the wavelet ψ against,for example, a given feature function, that is,by solving an optimization problem where thecoefficients are chosen to minimize the devia-tion from the feature function or some variancein the wavelet transformed signal. A methodthat includes the dictionary selection into theoptimization by means of a so–called greedyalgorithm is the computation of a Karhunen–Loève basis as described in (Mallat, 1999).

However, usually wavelet dictionaries aremore popular in the context of MRA–basedwavelet analysis, see (Rubinstein, Zibulevsky,& Elad, 2010) for a recent application with rel-evant references, which is not the topic of thispaper.

Wavelets as regularity detectors

In addition to time–frequency decompositions,wavelet also perform well as an analysis tool,cf. (Holschneider, 1995), since the are ableto detect singularities of a function via thedecay of the wavelet coefficients. This is,by the way, perfectly in accordance with theFourier spectrum as well: no function canhave infinitely high frequency content, f(ξ)

has to tend to zero as |ξ| tends to infin-ity, a fact passed around as the Riemann–Lebesgue–Lemma at mathematical campfires.Even more interesting, the rate in which theFourier transform tends to zero is closely re-lated to the smoothness of the transformedfunction, where smoothness has to be seen in

Figure 5: The scalogram from Figure 1. This time

focus on the vertical lines at the transition between

different tones in our “melody”.

the sense of differentiability again. The samehappens – no surprise – with wavelets: if thescale tends to zero, i.e., the frequency tends toinfinity, then the wavelet coefficients decay, butthey do so locally ! This means that in principle,i.e. up to some technical conditions,

|Wψf (x, s)| ∼ sα for s→ 0 (23)

if the function f is α times differentiable atx. The quite tricky details needed for a pre-cise and quantitative formulation of this state-ment can be found in the books by Holschnei-der (Holschneider, 1995) and Mallat (Mallat,1999), but do not expect things to be very sim-ple or easy to understand. Nevertheless, thephenomenon is easy to recognize in our chordexample which nicely illustrates also that phe-nomenon. Indeed, if we look at Figure 1, wesee that at every transition there is a thin butclearly visible vertical line. This line showswavelet coefficients that slowly fade to back-ground color, hence decay, but very slowly. Onthe other hand, they exactly belong to the po-sitions where the frequency of the sine toneschanges, i.e., where the first derivative has a



discontinuity even if the signal is continuousthere. Thus, wavelets can do local singular-ity detection but it is not hard to imagine thatthis becomes more tricky for non–artificial sig-nals since eventually one has to read asymp-totic decay off a finite signal.

Wavelets vs. Fourier

The difference between Fourier and wavelettransform can nicely be illustrated by yet an-other musical phenomenon which is known asbeats, cf. (Benade, 1960; Helmholtz, 1885)and is often used for the tuning of musical in-struments. Mathematically, it is just an imme-diate consequence of the simple trigonometricidentity

sinx+ sin y = 2 sinx+ y

2cos

x− y2

, (24)

which says that two pure sine tones with closefrequencies mix into a sine with the averagefrequency whose amplitude rises and falls likethe cosine of the difference frequency. If, forexample, we take a 440 Hz sine tone and ap-ply to it a 2 Hz amplitude modulation, thenwhat we would perceive is “beating” sound of440 Hz. The Fourier analysis, however, woulddetect two tones of 438 Hz and 442 Hz, re-spectively, and indeed this is what the com-puted Fourier transform on the left of Figure 6shows. In plot resolution, and that makes iteven worse, it looks almost like single, blurredpeak of 440 Hz, and it is very hard to de-cide whether this computation really showstwo peaks or a numerical artifact. The wavelettransform, on the other hand, represents thesignal as it is perceived, namely as a fre-quency band with periodic amplitude modula-tion. Even the frequency can be determinedquite accurately from the maximal entries in

Figure 6: Fourier and wavelet analysis of the beat phe-

nomenon. The original signal is a 440 Hz sine tone of

two seconds with a 2 Hz amplitude modulation. The

plots show the Fourier transform (above) and the Mor-

let wavelet spectrogram (below).

the spectrogram, but of course, the pictureshows a rather blurred frequency, by far lesssharp than the peaks in the Fourier transform.

The beat phenomenon can also be ob-served in the Gabor transform, at least aslong as the frequency resolution, that is, thelength of the analyzing window is chosenrelatively small. The more the size of the win-dow and thus the frequency resolution of itsFourier transform approaches the frequencyresolution of the original signal, the more theGabor transform behaves “Fourier like” withseparated frequencies. For small windows,



Figure 7: The Gabor transfor with a small (∼ 5% of the

frequency resolution) and mid–sized (∼ 12 % frequency

resolution window. The beat effect is slightly less with the

latter, but also the phase of the beat is shifted.

on the other hand, beats are displayed as asingle modulated frequency, see Figure 7 andFigure 8.

Keep in mind, however, that there is no“right” or “wrong” here as we simply look atthe left or right hand side of the trigonomet-ric identity (24). Both decompositions are validrepresentations of the original signal and bothrequire proper interpretation to be understoodin the right sense.

Figure 8: At a window size of half the frequency res-

olution the signal looks essentially like two separated

frequencies.

The finite world

As mentioned before, finite measurement orrecording is unavoidable in reality. After all,also the available resources, time, storage andpatience for example, are only finite. On theother hand, the integral in the wavelet trans-form (14) is an infinite one. Now, suppose thatthe wavelet ψ “lives” on the interval [−T, T ],then, to computeWψf(s, t), we need to know f

on the interval [t− sT, t+ sT ]. If t is now closeto the beginning or the end of the measure-ment of f , then this interval will exceed the re-gion where we know f and hence we will haveto fill in “phantom values” for f at these loca-tions where we do not know the function. Usu-ally, these values are either set to zero or takenfrom a periodic wrapping of f . Whatever wedo, there are values of s and t where we can-not trust the wavelet transform as it is based onvalues of f that are not known but are entirelybased on pure guesswork. And also note thatthis region grows if the scale grows! Depend-ing on the support of the wavelet, there is onlya U–shaped region of the scalogram of certain



size (the size depending on the support of thewavelet) where the results of the transform canbe trusted. It can even happen, if the supportof the wavelet is large and the considered fre-quency range to low, that all of the scalogramis contaminated by overlap artifacts. The valueof such a transform is easy to guess.

The discrete world

In practical signal processing one is not deal-ing with continuous functions, but with dis-crete data. Usually, our favorite piece of mu-sic is stored in a time–sampled fashion on aCD, EEG or other biosignal information arealso available as time discrete signals only.Such signals are sequences or functions onZ, the set of integers. Here Z takes thesame role as R in the preceding chapters ontime–continuous signals: even if realistic sig-nals are usually of a finite nature, they willbe embedded into this infinite domain whichhelps to avoid fiddling with boundary effects.The Fourier transform of a sequence f is thetrigonometric series

f(ξ) =∑k∈Z

f(k)eikξ, (25)

a 2π–periodic function. Note the (almost) per-fect analogy with the inverse Fourier transform(2) as the summation takes the role of “dis-crete integration”; in fact, the integral symbol∫

is only a “stylized” and “smoothed” versionof the summation symbol

∑. The interchange

of transform and inverse comes from the factthat usually, the Fourier coefficients of a 2π–periodic function g are

g(k) =1

2π

∫ 2π

0

g(t) e−ikt dt, k ∈ Z, (26)

but after all Fourier transform and its inverseare only distinguished by a complex conjuga-tion of the exponential term and this is obvi-ously exchangable. Nevertheless, (25) is notyet the discrete Fourier transform (DFT)! TheDFT is the vector obtained by sampling thetrigonometric series uniformly on [0, 2π]:

fn :=

[f

(2kπ

n

): k = 0, . . . , n− 1

]. (27)

However, there remains the question of howto choose the ‘sampling rate n. This is sim-ple if f is a finite signal, i.e., if it can bedescribed after an appropriate shift as f =

[f(j) : j = 0, . . . , n− 1]. Then the DFT is sim-ply a transformation that converts vectors oflength n into vectors of length n. And exactlythis is – once more up to normalization – whatis done in a most efficient way by the FFT, thefast Fourier transform. For the sake of maximalconfusion, we also write f ∈ Rn for the DFT ofa vector f ∈ Rn.

But whatever the DFT is - it is not the sam-pled version of the Fourier transform, henceno discrete spectrum, of the time–continuousfunction f whose discrete samples we claimto consider. Here is an example. Supposethat the discrete f is obtained by sampling atime continuous signal f∗ at equidistant pointstk = t0 + kh, k = 0, . . . , n − 1 with somesampling distance or reciprocal sampling rateh > 0:

f(k) = f∗ (tk) . (28)

Then the DFT is the vectorn−1∑j=0

f (tj) e2ijkπ/n : k = 0, . . . , n− 1

(29)

which has no obvious connection to the spec-trum of f . To understand what happens here,



it is useful to consider, for some function ϕ, thequasi interpolant

fϕ(t) =

n−1∑k=0

f(k)ϕ (t/h− k) , (30)

which is now a function again that, ideally, rep-resents or at least approximates f , hence canbe considered a “substitute” based on the dis-crete sampling information only. For example,if ϕ is the so–called hat function, then fϕ is thepiecewise linear function connecting the dis-crete values. Now, we can consider the Fouriertransform of fϕ and find that for the equidistantfrequencies ξk := 2kπ

nh we get

fϕ (ξk) = h ϕ

(2kπ

n

)f(k), k = 0, . . . , n.

(31)Here we finally find samples of a “real” Fouriertransform, however, we take that of fϕ and wehave to re–weight the spectrum with samplesof ϕ from the interval [0, 2π). It’s remark timeagain:

1. The frequency for the sampling of theFourier transform are taken from

[0, 2πh

),

so the higher the sampling rate 1/h, thelarger the frequency range. The fre-quency resolution, however, depends onthe number of samples, n. The morepoints we have, the larger the number ofdifferent frequencies and the smaller the(relative) distance between them.

2. Negative values of ξ play no role in whatwe do here. We always tacitly assumedthe signal to be real which means that itsFourier transform is symmetric.

3. The choice of ϕ clearly affects the spec-trum. “Natural” candidates would bepiecewise constant or linear functions or

general cardinal spline quasi–interpolants(Schoenberg, 1973) – whatever this is.They correspond to a stronger a strongerdamping of high frequency content asthey provide smoother and smoother ap-proximants. In some sense, the choicemust be made according to an under-lying model from which type of functionthe discrete data f is supposed to besampled.

4. Another choice would be

ϕ(t) = t =sinπt

πt.

The resulting function interpolates thedata f , i.e., fϕ (tk) = f(k), and if f issampled from a band–limited function(a function whose Fourier transform is 0

whenever the frequency satisfies |ξ| ≥ T

for some T ) and h is smaller than a so–called Nyquist rate, then we are evenguaranteed that fϕ is identical with thisfunction. This is the famous Shannonsampling theorem, cf. (Shannon, 1948),that rediscovered a result by Whittaker(Whittaker, 1915) and put it into the con-text of signal processing. In fact, thissounds even more perfect since normallyall records of data, for example audioor EEG date, are indeed bandlimiteddue to their acquisition method where atone place or another a low–pass filter isinvolved.

5. This sounds like the perfect solution, inparticular as ϕ is identically 1 for the val-ues in (31), so all of a sudden f can be di-rectly interpreted as samples of a Fouriertransform. So why bother at all? Sim-ply because Heisenberg objects: being



band limited, the underlying function can-not have finite support and so the finitelymany samples always miss some part ofthe function, hence causing artifacts.

6. But it is even worse! Though the func-tion is an interpolant and thus perfectlyapproximates at the sampling points, it isa very poor approximant when consideredaway from these points due to the ratherslow decay of that function. That meansthat the value at some point is still signif-icantly affected even by rather far–awaysamples, in particular the missing sam-ples that have been left out due to thefiniteness of the signal. So the theoret-ically perfect method can be numericallyvery questionable.

Nevertheless, we can quite efficiently com-pute samples of the spectrum of a functionfrom samples of the function, provided that theglobal difference between the function f∗ andfϕ is not too large. But the quality of this ap-proximation, i.e., the size of this distance, willdefinitely be affected by the choice of ϕ whichtherefore may be worth some thinking. All thisis far from new and well–known, cf. (Schüßler,1992), but rarely mentioned.

Summary

What was the point of this section? Thereare clearly a lot of techniques and methods towork with Fourier and wavelet transform andto perform time–frequency analysis but theirstrict validity depends on quite a few assump-tion that are hard or even impossible to checkor provide in reality. Consequently, the resultsof numerical computations should always betaken with a certain amount of care. And it

may pay off to invest some though about mod-els for the underlying functions from which thesamples are taken. Otherwise the price to bepayed is usually an overestimation of the high–frequency content of the signal.

Fast wavelet and inversetransforms

We now turn to the practical numerical com-putation of wavelet transforms. To that end,we assume that the function f∗ is only knownby samples as in (28), the normal situation inmost practical applications. Usually the sam-pling points are prescribed by technologicalside conditions and cannot be varied accord-ing to our needs.

The naive way to compute the wavelet trans-form would be to evaluate the integral from(14) by means of a quadrature formula, cf.(Gautschi, 1997), of the form

Wψf(u, s) ∼n−1∑k=0

f (tk)1√sψ

(tk − us

)wk,

(32)with appropriate weights wk, usually from themost popular family of so–called Newton–Cotes formulas, including the famous rect-angular and trapezoidal rules. If we want tokeep the spirit of the FFT and compute n

time samples uj , j = 0, . . . , n − 1, per scales, the computational effort of this computa-tion is O

(n2). The numerical quality of the

quadrature depends on the sampling dis-tance h (encoded in the tk) and the way howthe weights wk are chosen, which is usu-ally related to the (assumed) smoothness ofthe underlying f∗. “Better” quadrature tech-niques, like Gaussian quadrature rules, arenot available here, as they require a particular



non–uniform choice of the sampling points.In addition, it is not even clear whether an“improved”, higher order quadrature formulawill really be of advantage as such formulas’full power only occurs in connection with verysmooth signals. There is also the temptingidea of interpreting the wavelet as a weightfunction and encode it into suitably adaptedvalues wk, but since the admissibility conditionrequires at least one vanishing moment, suchquadrature would be built on an indefinite innerproduct and hence act without any theoreticalbackground or justification. That does notmean it would not work, it simply means that itcannot be guaranteed to work, at least not inthe “standard” environment.

FFT – the basis of everything

We have already defined the DFT of a vector oflength n in (27) as an operation that transformthe vector f into another vector f of the samelength n. Since this operation is linear, it canin fact be written as a matrix–vector multiplica-tion f = Vnf where the matrix Vn is a well–understood object with a rich and useful struc-ture. What interests us here, however, is thecost of computing f , that is, the number of el-ementary computational operations that haveto be performed. Since for every entry of f wehave to take an inner product between a rowof Vn and f , the cost of such a matrix–vectormultiplication appears to be n times the n mul-tiplications and n−1 additions that are neededfor such an inner product, leading to a total of2n2 − n operations. To make our lives easier,we introduce the “O notation”. Let F (n) be anyfunction measuring the cost of an operation,then we say that F is a O (G(n)) if there exists

a constant C > 0 such that

limn→∞

F (n)

G(n)= C.

In our example of matrix–vector multiplicationabove, the cost is O

(n2)

and the constant isa modest 2, and it seems as if there is nocheaper way to multiply a matrix and a vec-tor and so we are stuck with a complexity ofO(n2)

for the DFT. There is some truth in theabove statement as the cost of the multiplica-tion of a general n × n matrix with an n vec-tor is indeed O

(n2), but it is not true for the

DFT matrix. If its structure, which we praisedso highly before, is exploited in a proper way,then the DFT and hence this multiplication canbe computed with O (n log n) operations (andstill a very modest constant C). This extremelysimple method, (re)discovered by Cooley andTukey (Cooley, 1990, 1987; Cooley & Tukey,1965), is the basis of almost any fast algorithmfrom the multiplication of particularly structuredmatrices, so–called Toeplitz matrices, to thefast multiplication of large integers by meansof the Schoenhage–Strassen method (Gathen& Gerhard, 1999). Nevertheless, in order toreally emphasize and earn the first “F” in anFFT, lots of implementation details have to betaken into account, cf. (Loan, 1992), but for-tunately there exist very good and performantlibraries, be it open source ones like FFTW ornVidia’s CUDA library that even makes use ofthe graphics card to perform the computations.

What makes the FFT such a universal ac-celerator of computations is the fact that con-volutions appear quite frequently in scientificcomputations, even in our wavelet transform.In the continuous case, the convolution f ∗ g of



two functions f, g yields the new function

(f ∗ g) (t) =

∫Rf(s) g(t− s) ds

=

∫Rf(t− s) g(s) ds.

Again, it is easy to see that a naive computa-tion of such a convolution for n discrete sam-ples of f and g has a complexity of O

(n2).

If, on the other hand, we use the fact that theFourier transform of a convolution is

(f ∗ g)∧

(ξ) = f(ξ) g(ξ),

we can compute the convolution as well bymeans of a Fourier transform, pointwise mul-tiplication of these transformed values and fi-nally an inverse transform which, costs us2O (n log n) for the transforms andO(n) for themultiplication, summing up to a total cost ofO (n log n) operations. Very convincing, isn’tit, and that is indeed the way things work inthis as banal as powerful principle:

Whenever there is a convolution, useFFT and multiplication instead.

The magic word here is “in principle” as againwe thoughtlessly mixed the continuous and thediscrete universe. The DFT of sampled data isstill not a sampled Fourier transform, regard-less of whether we use fast or slow means ofcomputation and the truth is as follows: If f, gare two vectors of length n, then the compo-nentwise product of their DFTs indeed makessense, namely

f(k) g(k) = (f ∗n g)∧

(k),

where

(f ∗n g) (k) :=∑

j∈Z/nZ

fj gk−j .

The slight but fundamental difference lies inthe convolution which has to be understoodas a periodic summation where any indexk − j that is outside the admissible region0, . . . , n− 1 is “wrapped” into an admissibleone by adding a proper multiple of n. In otherwords: Whenever an FFT is computed, it as-sumes the input vectors f, g to be periodic. Ifthe are not, for example when a sound signal isnot sampled according to its frequency, therewill be artifacts tainting the result of the DFT.There are plenty of techniques in signal pro-cessing, zero padding for example, but nothingcan fully compensate the fact that, by its verynature, the DFT is tied to the periodic convolu-tion. So handle with care.

The fast wavelet transform

A faster and more efficient way to compute thewavelet transform makes use of the FFT. Thekey is a discretized version of (17) in which weonce more replace f∗ by fϕ and obtain by (31)that, for k = 0, . . . , n− 1,

(Wψfϕ (·, s))∧ (ξk)

=√sh ϕ

(2kπ

n

)f(k) ψ (sξk) , (33)

to which we can apply a fast inverse Fouriertransform to compute the vector

[Wψfϕ (tk, s) : k = 0, . . . , n− 1]

of n samples of the wavelet transform at thesame points as the original function was sam-pled. Since the complexity of the FFT and itsinverse is a cheap O (n log n) and since all theoperations in (33) are O(n), including the sam-pling of ϕ (which needs only be done once,independent of the scale) and of ψ, the total



computational effort of the fast wavelet trans-form (FWT) is still O (n log n) and thus signifi-cantly better than in the case of quadrature.

In (33) a sampling of ψ with different sam-pling rates, depending on the scale is required– which is, by the way, essentially the onlyscale–dependency in this formula. This sam-pling is very easy if the Fourier transform ofthe wavelet is explicitly known, like in the caseof our three examples before, and it even sug-gests that designing a wavelet is easier in theFourier domain. If the wavelet is only given intime domain, the values ψ (sξk) can neverthe-less be computed efficiently from a set of sam-ples ψ (stk) by yet another application of theFFT. This, however, requires a little bit of at-tention since the locations ξk from (31) dependon the sampling frequency and the number ofsamples which have to be chosen properly.

It should be said that an implementationof the FWT in a system like Matlab or itshigly recommendable free open source cloneoctave (Eaton, 2008) requires a little bit ofcare to correctly apply the fft and ifft com-mands and handle all the needed normaliza-tions correctly. There exists a stable imple-mentation by our Scientific Computing groupin Gießen that has been successfully appliedto various time–frequency tasks meanwhile.There exist other implementations of the con-tinuous wavelet transform that are based onresampling the function data or on computingthe wavelet transform integral (14) by meansof a more or less sophisticated quadrature for-mula. My experience on such implementa-tions is not very good, they are significantlyslower and any resampling of the function datamust almost necessarily lead to artifacts un-less more information is present on the nature

of the sampled function.

So far, one important question is left unan-swered: how to choose the frequencies. TheFWT computes each frequency separately, sothe frequencies (scales) can be chosen delib-erately. Taking into account the structure ofthe Heisenberg boxes for wavelets, the mostreasonable choice for the frequencies or, moreprecisely, scales, is to select the m scales un-der consideration as

sj = s0 σj , j = 0, . . . ,m−1, σ > 1, (34)

where σ is a parameter that should be smallerthan the size σ(ψ) of the Heisenberg boxes toavoid gaps in frequency. Such a type of inter-val scaling is once more perfectly compatiblewith music, where, in a tempered scale a semi-tone step corresponds to multiplication of thefrequencies by the factor 21/12. The closer σis chosen to 1 the larger the effort to computethe wavelet transform for given frequency bandbecomes since m = logσ

sms0

. The larger σ ischosen, on the other hand, the worse the ab-solute frequency resolution becomes for highfrequencies. Hence, an appropriate choice ofthe parameters s0, σ and m is fundamental inapplications and depends on the wavelet func-tion, the frequency band to be considered aswell as the accuracy one aims for. Anyway, thetotal computational complexity of the FWT form scales from n samples is O (mn log n).

The fast inverse transform

For the inverse transform, we accelerate thecomputation of (15) by noting that the “innerintegral” over u is yet another convolution andcan thus be computed in terms of the FFT: withg∗(t, u) = Wψf(t, u), known from g(k) = g (tk),



k = 0, . . . , n− 1, we get as before that

h(k, s) :=

(∫Rgϕ(u)ψ

(· − us

)du

)∧(ξk)

=√s h (g (·, u))

∧(k) ψ (sξk) , (35)

for k = 0, . . . , n − 1. For any j = 0, . . . ,m − 1,we can then compute the vectors

[h (k, sj) : k = 0, . . . , n− 1]

by means of an inverse FFT and from that ap-proximate

f (tk) =

∫Rh (k, s)

ds

s2∼

s−1∑j=0

h (k, sj) wj (36)

with weights wj of a quadrature formula forthe integral

∫dss2 with respect to the knots sj .

Specifically, if we set sj = s0σj and use the

rectangular rule, then

wj =

∫ sj+1

sj

s−2 ds

= −1

3s−30

(σ−3j−3 − σ−3j

)=

s−3j3

(1− σ−3

),

hence, in vectorized form,

[f (tk) : k]

∼ 1− σ−3

3

m−1∑j=0

s−3j [h (k, sj) : k] . (37)

Again, this operation has a total computationalcost of O (mn log n), just like the FWT andonce more a working implementation has tocarefully take into account some more detailslike how to correctly apply an FFT routine, butthe principle of the IFWT should be clear fromthe above exposition.

To some surprise, after reconsidering (33)the question arises why and whether such acomplicated method with all this quadrature

stuff in it will appear. The simple observationis that (33) can be rewritten as

f(k) =(Wψfϕ (·, s))∧ (ξk)√shϕ (2kπ/n) ψ (sξk)

, (38)

so that f can be reconstructed from a sin-gle scale s provided that ψ (sξk) 6= 0 for k =

0, . . . , n−1 which will usually work for k 6= 0, atleast for the Mexican hat (20) and the (mod-ified) Morlet wavelet – the Fourier transformof the (non–admissible) expression from (21)even has no zero at all. Numerically, there aretwo immediate arguments in favor of the inver-sion rule (37):

1. For small values of k, i.e., for low frequen-cies, the denominator in (38) will alwaysbe small; after all, ψ should be continu-ous as ψ should be at least integrable, andψ(0) = 0, so that any errors made in a pre-ceding wavelet transform will be amplifiedand the low frequency content f(k) willnot be very trustworthy. Practically, thismeans, that f could be modified by a moreor less random constant term. This effectcan be mildened by reconstructing f froma very large value of s, i.e., from a ratherlow frequency content, but then the cor-responding Heisenberg box tells us thatwe use information with very poor timelocalization, loosing the benefits of time–frequency analysis.

2. Since the first step, (35) uses only mul-tiplications and since ψ decays to ±∞,hence is bounded, it already saves us theworries about divisions by zero or almostzero. Moreover, (37) is an averaging pro-cess which we can hope to milden somerandom error made in the computation ormanipulation of the wavelet transform.



Numerically, the decision is clear, but there isa more substantial theoretical catch why theinverse transform should never use a formulalike (38), since we are inverting something thatactually cannot even be inverted in general. Toget some idea what goes on there and to studythe phenomenon without the influence of nu-merical effects, we return to the case of con-tinuous transform

Invertibility and loss of information

If the wavelet is admissible, the process ofwavelet transform (14) followed by its inversion(15) is an identity – as it should be. In termsof (14) and (16), this means that MψWψ = I,that is, Mψ is a left inverse of Wψ. The con-verse, WψMψ = I, does not hold true, how-ever, as not any function in two variables is awavelet transform. Intuitively, this appears rea-sonable since we cannot expect one dimen-sional curves to generate a two dimensionalset of transforms: while the function f dependson only one variable t, the wavelet transformWψf has two variables, u and s, and it ap-pears at least strange (though this is not im-possible as the concept of so–called space fill-ing curves, also known as Peano curves, cf.(Gelbaum & Olmstedt, 1964), shows) that aunivariate curve should be the same as a bi-variate “surface”. Intuition, however, can bemisleading, so we need a more sensible ar-gument.

The key to a proof of this observation is (17).If s and s′ are two scales, then it follows that

Wψf (u, s′)

=

√s′

s

(ψ (s′·)ψ(s·)

(Wψf(·, s))∧ (·)

)∨(u).

In other words: if we know one scale of the

wavelet transform, we know all of them (atleast if the Fourier transform of the waveletdoes not have “nasty zeros”). On the otherhand, any bivariate function g(u, s) that doesnot satisfy the compatibility condition

(g(·, s))∧ (ξ)

(g (·, s′))∧ (ξ)=

√s

s′ψ (sξ)

ψ (s′ξ)(39)

cannot be a wavelet transform, even if the in-verse wavelet transform applied to this functionis still well–defined and thus can be computed,at least numerically.

So what happens now, if we compute in-verse transforms with our beautiful numericalalgorithm? Suppose that g(u, s) is a givenfunction of two variables, maybe obtained frommodifying a wavelet transform with some sortof time localized band pass filter. If we re–transform our inverse wavelet transform, weobtain a function g = WψMψg which now isa wavelet transform and hence satisfies thecompatibility condition (39). To understand therelationship between g and g we apply the in-verse transform to the difference, yielding

Mψ (g − g) = Mψg −MψWψMψg

= Mψg −Mψg = 0,

since MψWψ = I. As simple as this compu-tation appears and in fact is, it tells us whatgoes on in the inverse transform for which g

and g are indistinguishable. Now, for any g

there always exists such a compatible g withg = g if and only if g is compatible. Allfunctions g that lead to the same compatibleg are undistinguishable for the inverse trans-form, they form what is called an equivalenceclass and g is the compatible representer ofthis equivalence class. Clearly, each two dif-ferent compatible functions belong to differ-



Figure 9: A test signal (above) and its WψW−1ψ

transform (below). Obviously not an identity.

ent equivalence or, as one might say it, de-fine a class of their own. And now it is clearwhat happens: the inverse wavelet transformalways computes the inverse transform of theunique compatible representer in the equiva-lence class.

Let us consider this effect by means of anexample. To that end, we define a completelylocalized signal by means of its wavelet trans-form as in Figure 9 and then transform thiswavelet transform back and forward again. It isnot hard to see that this is not really an identity.While the support remains similar, the “inner”information vanishes. To say it in the terminol-ogy from above, the left hand side of Figure 9shows one element from the equivalence class

Figure 10: The truncated melody

while the right hand side shows the represen-ter of this class defined by WψW

−1ψ .

The second example is using the “melody”from Fig 1, where we remove the lowest tonefrom the “chord” at the end. As the scalogramshows, the result is almost perfect, however, aplot of the signal and of the error would showthat the modified signal is scaled differently.This is no surprise! The wavelet transform isan isometry, i.e., preserves energy, and anycontent we remove, be it on the function or onthe transform side, reduces the energy on theother side as well. Hence, the resulting signalmust have lower energy content which is dis-tributed equally over the whole signal by theinverse wavelet transform. And even this is un-derstandable from a brief but slightly carefullook at the inversion formula (15) which con-tains an averaging process over all scales.

Finiteness and the loss of information

In (22) we introduced the concept of vanishingmoments of a wavelet and sold it as somethingdesirable, which it is, at least in principle. Actu-ally, the regularity estimation in (23) works onlyif the number of vanishing moments of ψ ex-



ceeds α. Hence, to detect corners (i.e. singu-larities in the first derivative), the wavelet hasto have at least two vanishing moments – an-other good reason for the nature of the mexi-can hat wavelet. On the other hand, a waveletwith a certain number of vanishing momentsdestroys a certain polynomial content of thesignal. This is irrelevant in the sense of L2–functions since the only polynomial in L2 is thezero function, while for finite signals the effectof loss of constants, or more precisely loss ofkernel can be quite dramatic in reality. Con-sider a noisy parabola, i.e. a quadratic functionthat is modulated by some random noise, see

Figure 11: A toy signal (above) and what an identity

makes of it (below). The noisy parabola is simply trans-

formed and then put into the inverse transform. The result

is not really perfectly similar to the original signal.

Figure 12: The wavelet transform of both signals from

Figure 11 (above). Except the “artifact” part outside the

U–shaped interior region, it contains no low frequency

information which is due to the fact that the parabola

is “killed” by the vanishing moments of the underlying

wavelet, in this case he morlet wavelet. This image also

shows how noise appears in wavelet transforms: as quite

random peaks in the high frequency part. The “recon-

struction signal” f −W−1ψ Wψf (below) consists of the

“lost parabola” from Figure 11 plus some high frequency

noise that was beyond the frequency band of the original

signal.

Figure 11. The explanation can be found in thewavelet transform depicted in Figure 12 whereit is visible that the parabola content is essen-tially removed by the vanishing moments of thewavelet. Nevertheless, such effects can quiteeasily be compensated when doing the time



local bandpass filters in the following section.Starting with a signal f , one first computes theinformation loss

∆ψf :=(I −W−1ψ Wψ

)f, (40)

then performs manipulations on the wavelettransform Wψf , leading to function g, say, andthen uses a back transformation of the form∆ψf +W−1ψ g.

But again keep in mind that according to the-ory ∆ψ should be zero, the occurence of sucherrors is a pure finiteness artifact which can beas nasty as it is unavoidable in reality or when-ever an infinite theory (on the real line R) isapplied to finite data.

Time local bandpass filters

Probably one of the most appealing applica-tions of time frequency analysis and a numeri-cal inverse wavelet transform is the implemen-tation of time localized bandpass filters. Again,the musical analogy helps to understand thebasic idea of this concept. Suppose that in ourpiece of music a wrong key has been playedand this needs to be corrected. In other words,for some relatively short period of time, the fre-quency content needs to be modified. This canbe done by “cutting out” some frequencies and“filling in” some others. Of course, we can-not expect the resulting scalogram to satisfythe compatibility condition (39) and hence, theresult is not a valid wavelet transform, so thatthe resulting signal will not be only the inversewavelet transform of the compatible represen-ter of the equivalence class. How bad is that?Not so bad normally, as the following reason-ing shows.

Suppose we have done a local modifica-tion, i.e., we replaced g = Wψf by g + h

where the correction function h is zero every-where except a small square of side lengthδ around u∗ and s∗ which leads to (41).

Since the “-let” of a good wavelet verbal-izes the fact that the function ψ(x) decays(rapidly) for x → ±∞, we can assume thatalso ψ only “lives” on a bounded interval in thesense that outside that intervall, say [−T, T ],ψ is at least neglectable. Hence, the integralabove is only relevant for those values of tsuch that t− u ∈ s[−T, T ] or

t ∈ [u∗ − Ts− δ, u∗ + Ts+ δ]

an interval around u∗ of essential width 2Ts.Hence, if s is a small scale, hence correspondsto a high frequency, then the modification es-sentially remains located around u∗ while forlarge values of s, i.e., low frequencies, themodification leaks out as might be expected.However, the s−2–weighting of the integral in(41) “dampens” the effect and the wider thespread is, the larger the damping is – one moregood reason to use this averaging formula forinversion. So essentially the modification re-mains at least local in time. A similar argu-ment applied to the Fourier transform of theinverse transform in the same way as in theproof of the inverse formula, cf. (Daubechies,1992; Mallat, 1999), also can be used to rea-son for localization in frequency. A more pre-cise and mathematically relevant formulationof this phenomenon clearly has to take into ac-count and will depend on the rate of decay ofthe wavelet ψ and other parameters.

What did we find here? There was noassumption made on the correction term h,in particular we did not require compatibility,and nevertheless the inverse wavelet trans-form modified f mainly locally around the



Mψ (g + h) (t) = f(t) +1

Cψ

u∗+δ∫u∗−δ

s∗+δ∫s∗−δ

h(u, s)1√sψ

(t− us

)du

ds

s2. (41)

time–frequency region where the wavelettransform was modified. This makes “scalo-gram surgery” quite a useful tool – at leastheuristically.

It should, however, be emphasized oncemore that this is entirely a “locality” argument.Just look at Figure 9 to realize that both trans-forms show a signal that is local in time andfrequency, but still quite a bit different.

Summary

In general, time–frequency analysis, be it Ga-bor or wavelet style, is a useful tool for biosig-nal processing that definitely extends the pos-sibilities of the Fourier transform. The priceto be payed is a significantly higher complex-ity – each single scale costs about as much asa Fourier transform – and some mathematicalintricacies that should be understood, at leastintuitively, to avoid certain pitfalls. Those pit-falls and their mathematical explanations werethe goal of this paper. It is not necessary anymore to advertise the wavelet transform or theGabor transform as they are powerful tools, butit seems appropriate to show the limitations ofthese tools and to clarify how the results ob-tained by these tools have to be interpretedproperly. The nice side effect is that music, avery popular sort of signals, can be used forexplanations that are more intuitive than theapplication of the methods to biosignals like,for example, EEG data.

It would be tempting to make some remarksabout existing wavelet toolboxes, but I want to

avoid it. First, such statements can only bemomentary snapshots and may change withthe next release of the software. Second, anmore important, most commercial systems donot offer insight into the precise implementa-tion of the toolboxes so that the quality and cor-rectness of the results simply can only be be-lieved or not and everything else would mostlybe speculation. This even starts with suchelementary questions as whether the Morletwavelet is used with our without the correctionterm, i.e., whether it is a wavelet at all, and ex-tends to points like handling of resampling orpadding issues. There are choices to be madeand these choices affect the result.

The same holds for many of the paperswhere wavelets are applied to some problem,for example from physiology as, for example,in (Samar, Bopardikar, Raghuveer, & Swartz,1999). Normally, such papers only give a def-inition of the wavelet transform like in (14) anda set of colored pictures from which conclu-sions are drawn, and not even (Klein, Sauer,Jedynak, & Skrandies, 2006) is an exceptionthere. It is seldom even mentioned how andby which software these transforms were com-puted and those pictures were generated, sothat it is mostly impossible to make any state-ments about these results and it would be un-fair to judge the results based on such specu-lations.



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W. Skrandies — Abstracts of the 19th German EEG/EP Mapping Meeting

Abstracts of the 19thGermanEEG/EP Mapping Meeting,Giessen, October 15 - 17,

2010

The monofractal signature of EEG mi-crostates reveals rapid dynamics ofresting-state networks. J. Britz (1,2), D.van de Ville (3,4), C. M. Michel (1,2,5), (1)Department of Fundamental Neuroscience,University of Geneva, Geneva, Switzerland(2) EEG Brain Mapping Core, BiomedicalImaging Center (CIBM), Geneva, Switzerland,(3) Department of Radiology and MedicalInformatics, University of Geneva, Geneva,Switzerland (4) Institute of Bioengineering,Ecole Polytechnique Fédérale de Lausanne,Switzerland, (5) Department of Neurology,University of Geneva Medical School, Switzer-land

Resting-state functional connectivity studieswith fMRI show that the brain is intrinsicallyorganized into large-scale functional networks(RSNs) for which the hemodynamic signatureis stable for about 10 s. Spatial analysesEEG topography at rest also show discreteepochs of stable global brain states (so-calledmicrostates), but they remain quasi-stationaryfor only about 100 ms. In order to test the rela-tionship between the rapidly fluctuating EEG-defined microstates and the slowly oscillatingfMRI-defined resting states, we recorded theEEG from 64 channels in the scanner whilesubjects were at rest with their eyes closed.Conventional EEG-microstate analysis deter-mined the typical four EEG topographies that

dominated across all subjects. The convolu-tion of the time course of these maps with thehemodynamic response function allowed to fita linear model to the fMRI BOLD responsesand revealed four distinct distributed networks.These RSNs have previously been attributeto auditory processing, visual processing, at-tention reorientation, and subjective interocep-tive autonomic processing. Surprisingly, theconvolution with the HRF did not remove anyinformation-carrying signal from the microstatesequence. The microstate sequences showedthe same relative temporal behavior beforeand after convolution with the HRF, i.e. at tem-poral scales that are two orders of magnitudeapart, which suggests that their time courseis scale-free. We deployed powerful wavelet-based fractal analysis that allowed determin-ing scale-free behavior. We found strong ev-idence that microstate sequences are scale-free over 6 dyadic scales covering the 256ms16s range. The degree of long-range depen-dency was maintained when shuffling the localmicrostate labels but became indistinguishablefrom white noise when equalizing microstatedurations, which indicates that temporal dy-namics are their key characteristic. Taken to-gether, the four typical EEG microstates seemto represent the neurophysiological correlateof four RSNs and their monofractal character-istics show that they are fluctuating much morerapidly than fMRI alone suggests.

Topographic EEG signatures of fMRI rest-ing state networks. K. Jann (1), M. Kottlow(1), T. Dierks (1), C. Boesch (2), T. Koenig(1), (1) Department of Psychiatric Neurophys-iology, University Hospital of Psychiatry, Uni-versity of Bern, Bern, Switzerland, (2) Depart-ment of Clinical Research (AMSM), Inselspital



and University of Bern, Bern, SwitzerlandThe temporal fluctuations of fMRI RestingState Networks (RSNs) have been demon-strated to be correlated to the spectral fluc-tuations in several EEG frequency bands.However, there is no study accounting for thetopographic distribution of EEG oscillations. Inthis study we explored the topography of spec-tral fluctuations associated to ten commonRSNs. Therefore we recorded simultaneousEEG-fMRI in 20 healthy young subjects. Wepresent topographic maps (covariance andt-maps) for all RSNs displaying their specificspatial EEG spectra in the standard EEGfrequency bands.

It’s a face - Continuous face integration incombined EEG/fMRI. M. Kottlow, K. Jann, T.Dierks, T. Koenig, Department of PsychiatricNeurophysiology, University Hospital of Psy-chiatry, University of Bern, SwitzerlandHumans tend to automatically bind facial com-ponents into a face gestalt, making face per-ception a natural example for the analysis offeature binding. It is assumed that face pro-cessing involves specific brain regions includ-ing the fusiform face area and that binding de-pends on the synchronization of EEG frequen-cies in the gamma range. Here we integratedthese findings by correlating gamma synchro-nization with BOLD responses. We presentedunpredictably moving elements of a schematicface, which during some periods continuouslyproduced a complete facial percept, represent-ing analytic and holistic face processing. Dur-ing holistic processing, the complete uprightface is integrated to a face gestalt, while duringanalytic processing the spatial order of a faceis disturbed and the face has to be composedpart-by-part. As hypothesized, we found in-

creased gamma phase synchronization dur-ing holistic face processing. BOLD responseswith emphasis on the right fusiform face areawere similar during both conditions. Finally,the standard boxcar predictors for each condi-tion were modulated with gamma synchroniza-tion revealing a holistic face network compris-ing face perception regions, and an analyticnetwork including parietal and prefrontal ar-eas but not the fusiform gyrus. The precuneuswas present in both networks. Thus, althoughthe FFA is involved in both analytic and holis-tic binding, the modulation with gamma oscilla-tions suggests different roles depending on thecondition. The precuneus in contrasts seemsto be involved in binding processes in general.Hence, the combination of BOLD responsesand gamma phase synchronization may helpto decode the functions of brain areas withinnetworks.

EEG-BOLD coupling and brain develop-ment. R. Lüchinger, Department of Childand Adolescent Psychiatry University Zurich,Zurich, SwitzerlandThe development of the human brain is char-acterized by profound structural and functionalreorganization. Using EEG, brain maturationhas been studied since decades. The rest-ing EEG is typically characterized by oscilla-tions of different frequencies and amplitudes,reflecting ongoing neuronal activity. Duringdevelopment the EEG frequency compositionchanges dramatically. In recent years co-registering EEG and fMRI has allowed for link-ing electrophysiological scalp-recorded activitymore directly to underlying cortical and sub-cortical regions without assumptions regardingsource distribution. While the exact physiolog-ical relationship between EEG and the fMRI



blood oxygen-level dependency (BOLD) sig-nal is still under debate, these studies haveshown that EEG amplitude is functionally cou-pled to distinct brain regions and networks.However, in the emerging field of simultane-ous EEG-fMRI research, little is known aboutthe development of EEG-BOLD coupling. BothEEG and fMRI are sensitive for maturationalchanges, but capture partly different neuronalsignals, witch presumably indicate different as-pects of brain development. We aim to char-acterize changing and sustaining features ofEEG-BOLD coupling pattern in the develop-mental course.

EEG-fMRI investigation of gamma oscilla-tions. C. Mulert, Psychiatry NeuroimagingBranch (PNB), Department of Psychiatry /NeuroImage Nord (NIN) UKE Hamburg, Ger-manyNeuronal oscillations in the gamma-band fre-quency range have attracted much interestduring the last few years because they weresuggested to play an important role in thelinking of neurons into cell assemblies thatcode information in the brain. Experimentaldata obtained both in animals and in humanssuggest that gamma-band oscillations are in-volved in perception and cognition. In addi-tion, disturbed gamma oscillations might be re-lated fundamental pathophysiological aspectsof schizophrenia. This talk will focus on re-cent results using single trial coupling of thegamma-band response (GBR) and the BloodOxygenation Level Dependent (BOLD) signal.Furthermore, data of disturbed GBR in pa-tients with schizophrenia and unaffected sib-lings will be presented and discussed with re-gards to implications for the understanding ofdisturbed brain mechanisms in schizophrenia.

Exploring the functional role of intrinsicbrain states by simultaneous EEG-fMRI. P.Ritter, Abteilung für Neurologie, Charite, Uni-versity Medicine Berlin, GermanyFunctional magnetic resonance imaging(fMRI) measures neuronal activity not directlybut relies on associated blood oxygenationchanges. Electroencephalography (EEG) incontrast assesses neuroelectric populationactivity. We use simultaneous EEG-fMRI inorder to investigate the relation between ongo-ing EEG signatures such as the alpha rhythmand the fMRI signal. We show that ongoingEEG dynamics influence not only the intrinsic(’resting state’) fMRI signal but also determinefMRI response properties to visual stimulation.

Simultaneous EEG-fMRI. D. Brandeis, De-partment of Child and Adolescent Psychiatry,University of Zürich, Zürich, Switzerland, Cen-ter for Integrative Human Physiology, Univer-sity of Zürich, Zürich, Switzerland, Departmentof Child and Adolescent Psychiatry and Psy-chotherapy, Central Institute of Mental Health,Mannheim, GermanyThe symposium contributions cover the widerange of current applications of simultaneousEEG - fMRI recordings. Recent work has in-creasingly moved away from just concentrat-ing on the advantage of combining high spatialand temporal resolution. One trend is to fo-cus on the spontaneous dynamics of the back-ground or resting state, and their interactionswith stimulation and factors affecting the na-ture of the coupling between EEG and BOLDsignals. Another recent trend is to focus onhow the dynamics of spontaneous or event-related trial - to trial fluctuations of oscillatoryactivity interact with the dynamics of percep-tion and cognition, and understand clinical and



genetic variations. The dynamics of the restingstate are typically characterized by correlatedBOLD fluctuations or by EEG power fluctua-tions, but both Britz and Jann show that spe-cific EEG microstates or topographies moreclosely correspond to the BOLD fluctuations.Resting state studies the first part address howvariations of the “backgroundresting state de-fined by the EEG affect the BOLD responseto visual stimulation is addressed by Ritter etal, and how development affects the couplingbetween resting state EEG and BOLD is pre-sented by Lüchinger.The dynamics of gamma oscillation and theirBOLD correlates are addressed in two con-tributions. Mulert focuses on event-relatedgamma oscillations in schizophrenia and dis-cusses clinical alterations and familiality, whileKottlow demonstrates that gamma synchro-nization identifies those elements of the BOLDnetwork involved binding coherent perceptsduring holistic face perception. In conclusion,these contributions illustrate how EEG-fMRIhas progressed from focusing on mutual vali-dation and on understanding epileptform activ-ity to clarify basic physiological, cognitive andclinical aspects of brain function.

Spontaneous brain activity and EEG mi-crostates. A novel EEG/fMRI analysis ap-proach to explore resting-state networks.F. Musso, J. Brinkmeyer, LVR-Klinikum Düs-seldorf, Kliniken der Heinrich-Heine UniversitätDüsseldorf, Düsseldorf, GermanyThe brain is active even in the absence ofexplicit input or output as demonstrated fromelectrophysiological as well as imaging stud-ies. Using a combined approach we mea-sured spontaneous fluctuations in the bloodoxygen level dependent (BOLD) signal along

with electroencephalography (EEG) in elevenhealthy subjects during relaxed wakefulness(eyes closed). In contrast to other studieswhich used the EEG frequency information toguide the functional MRI (fMRI) analysis, weopted for transient EEG events, which iden-tify and quantify brain electric microstates astime epochs with quasi-stable field topogra-phy. We then used this microstate informationas regressors for the BOLD fluctuations. Sin-gle trial EEGs were segmented with a specificmodule of the LORETA (low resolution elec-tromagnetic tomography) software package inwhich microstates are represented as normal-ized vectors constituted by scalp electric po-tentials, i.e., the related 3-dimensional distri-bution of cortical current density in the brain.Using the occurrence and the duration of eachmicrostate, we modeled the hemodynamic re-sponse function (HRF) which revealed BOLDactivation in all subjects. The BOLD activa-tion patterns resembled well known resting-state networks (RSNs) such as the defaultmode network. Furthermore we cross vali-dated the data performing a BOLD indepen-dent component analysis (ICA) and comput-ing the correlation between each ICs and theEEG microstates across all subjects. Thisstudy shows for the first time that the infor-mation contained within EEG microstates ona millisecond timescale is able to elicit BOLDactivation patterns consistent with well knownRSNs, opening new avenues for multimodalimaging data processing.

EEG source analysis improves interpreta-tion of fMRI results obtained during EEG-fMRI of epileptiform discharges. M. Sini-atchkin (1), A. Galka (1), R. Boor (2), F. Moeller(1), J. Moehring (1), L. Elshof (1), K. Groen-



ing (1), S. Wolff (1), L. Hamid (1), U. Stephani(1,2), (1) Klinik für Neuropädiatrie, UniversitätKiel, (2) Norddeutsches Epilepsiezentrum fürKinder und Jugendliche, Raisdorf

Simultane Aufnahmen von EEG und funk-tionellem MRT ist eine neue Methode, die zurCharakterisierung hämodynamischer Verän-derungen im Gehirn, die im Zusammenhangmit epileptiformen Entladungen auftreten, be-nutzt werden kann. Diese Methode wurdeerfolgreich angewandt sowohl zur Beschrei-bung der epileptogenen Zone und der Prop-agationswege der epileptischen Aktivität beifokalen Epilepsien als auch zur Darstellungepileptischer neuronaler Netzwerke bei ver-schiedenen Epilepsie-Syndromen. Aufgrundder niedrigen zeitlichen Auflösung von fMRTund dem Problem der statistischen Schwellefür multiple Vergleiche bei Multivoxelanaly-sen, zeigt fMRT häufig eine ausgedehnte undkomplexe Aktivierung, die in vielen Fällennur schwer interpretierbar ist. Diese Studieillustriert an einer Reihe von Beispielen, wieeine EEG-Quellenanalyse (LAURA-Verfahren,implementiert in Cartool, Genf) hilft, fMRT-Ergebnisse zu interpretieren. 260 Kinderim Alter von 3 Monaten bis 18 Jahren mitfokalen und generalisierten Epilepsien wurdenmittels EEG-fMRT untersucht. Bei fokalenEpilepsien konnte die EEG-Quellenanalysebei 60% der Patienten die Gehirnregionen derinitialen epileptischen Aktivität (Generatoren)von den Gehirnregionen der Propagation tren-nen. Bei Patienten mit Continuous Spikesand Waves during Slow Sleep (CSWS) zeigtedie Quellenanalyse, dass das für diesesepileptische Syndrom typische Netzwerk (einebilaterale Aktivierung in einer perisylvischenGehirnregion und im anterioren Cingulum) die

propagierende epileptische Aktivität darstellt.Bei Absence-Epilepsie scheint die EEG-Quelleim medialen präfrontalen Kortex das Netzwerkzu dominieren, andere Quellen (frontaler undparietaler Kortex sowie Thalamus) sind engmit der primären Quelle verbunden (kohärenteQuellen). Ohne die Quellenanalyse lässtsich die Hierarchie und Aktivierungsreihen-folge von unterschiedlichen Gehirnregionenbei Absencen kaum erklären. Damit scheintdie Kombination von EEG-Quellenanalyseund fMRT komplimentäre Informationen zuliefern, die komplexe neuronale Netzwerke beiEpilepsien präzise beschreiben können.

Ghost Sources due to Spherical Head Mod-els: Do they exist? M. Wagner, M. Fuchs, J.Kastner, R. Tech, Compumedics Neuroscan,Hamburg, GermanyIt is generally acknowledged, that in EEGsource localization, the use of a spherical headmodel (as opposed to a realistically shapedhead model) introduces errors in the com-puted source locations. But can the choiceof head model also influence the more gen-eral characteristics of a dipole solution, suchas the number of assumed sources? Single-and multi-dipole data sets for sources of ran-dom locations and orientations were createdusing a three-layer realistic boundary elementmethod (BEM) head model. Noise was added.These data were then subjected to single-and multi-dipole analyses, assuming a real-istic head model in one case and a spheri-cal head model in the other case. Differentstrategies for determining the number of activesources were employed and compared in bothcases. Strategies explored involved the abilityof a dipole configuration to explain the signalpart of the data, as well as the shapes of the



dipoles’ confidence ellipsoids. The number ofdipoles required to explain a given data pointtended to be larger in the spherical head modelcase than in the realistic head model case orthe simulated ground truth. Such additionalsources do not account for features in the databut for inadequacies of the head model used.

Cortical generators following noxiuoslaser stimulation as identified by sourceanalysis from subdural grid recordings inhumans. U. Baumgärtner, S. Ohara, R.-D.Treede, F. Lenz, Lehrstuhl für Neurophysi-ologie, Medizinische Fakultät Mannheim derUniversität Heidelberg, Mannheim, Deutsch-land; Department of Neurosurgery, JohnsHopkins University, Baltimore, MD, USAThe role of the primary somatosensory (S1)cortex in nociceptive processing has been un-der debate for a couple of years (Apkarian etal. 2005, Eur J Pain 9: 463-84). Dipole sourceanalyses of laser evoked potentials (LEP) fromsurface EEG or MEG recordings as well assingle channel analysis of LEP obtained fromsubdural recordings in epilepsy patients sup-port the view that S1 contributes in a rele-vant manner to the perception of pain. Incombining LEP recordings from subdural gridswith dipole source analysis we now aimed tolocalize the early generators more precisely.Noxious infrared laser stimuli were appliedto the hand dorsum of two patients that un-derwent neurophysiological evaluation prior toepilepsy surgery. Subjects were awake andhad to count the stimuli. LEP recordings wereobtained from an 8 x 8 electrode grid (64channels) which was implanted in the subdu-ral space over the frontal lobe and coveredthe central sulcus as well as the sylvian fis-sure. After averaging the peri-stimulus seg-

ments (500ms pre, up to 1000 ms post stim-ulus, digitized at 1 kHz) and matching of theCT and MRI coordinate systems of the pa-tients, dipole source analysis was performed(BESA R©). The global field power yielded twomajor peaks (at 140 ms and at approx. 230ms), during which we performed the initial fitprocedure with regional sources. In both sub-jects, similar sources with a radial orienta-tion and peak activity at approximately 140 mswere identified within S1 cortex in parallel witha source in the suprasylvian region. In one ofthe subjects, the early radial S1 source was fol-lowed by activity of a tangential source 60-70ms later at almost the same position. The ra-dial LEP sources were found to be at or slightlyposterior to the individual central sulcus andthe localization of the N20 source as obtainedfrom analysis of median nerve SEP (as neu-rophysiologic marker for area 3b). Hence, weconclude that the LEP generator in this corti-cal region is localized most likely in Brodmannarea 1, where nociceptive neurons have beenidentified in monkey (cf. Kenshalo and Isensee1983, J Neurophysiol 50: 1479-96).This study was supported by NIH (NS 38493 to FAL)

and DFG (Tr236/13-4)

Cerebral processing of itch: EEG and MEGstudies. H. Mochizuki, Lehrstuhl für Neuro-physiologie, Medizinische Fakultät Mannheimder Universität Heidelberg, Mannheim,DeutschlandItch is an unpleasant sensation with the de-sire to scratch. Previous studies using PETand fMRI identified brain regions activated byitch stimuli, such as the somatosensory cor-tex, cingulate cortex, insula, parietal cortex,frontal cortex, basal ganglia and cerebellum.However, temporal information of itch stimulus-



related neural activity in these regions is stillunclear. Recently, the methodology to induceitch sensation by applying electrical stimulusto the skin with a certain condition (pulse du-ration > 2 ms, frequency > 50 Hz) throughelectrodes was developed (electrical induceditch). In a preliminary study, we confirmedthat it is possible to measure brain responsesassociated with the electrical induced itch us-ing EEG and also found that the electrical in-duced itch is associated with C-fibers. In thepresent study, we compared brain responsesbetween itch and pain by collecting MEG datafrom 10 healthy volunteers. Itch sensation wasevoked by stimulating the C-fibers using theelectrode discussed earlier while C-fiber painwas evoked by laser. The dipoles associatedwith itch stimulus- and pain stimulus-relatedmagnetic responses were mainly located inthe contralateral and ipsilateral secondary so-matosensory cortex / insula (SII/insula) andparietal cortex. The peak latency in contralat-eral SII/insula was significantly shorter thanthat in ipislateral one in itch and pain stimulusconditions. The location of dipole in SII/insulawas not significantly different between itch andpain. The peak latency in the parietal cortexwas significantly longer than that in the con-tralateral SII/insula only in pain stimulus condi-tion. Interestingly, in the parietal cortex, the lo-cation of the dipole related to itch stimulus wassignificantly more medial than that related topain stimulus. This finding suggests that theremay be some difference in processing in theparietal cortex between itch and pain.

Delay-dependent changes in oscillatorydelta, theta and alpha activity during recog-nition. B. Mathes (1,2), J. Bagdasaryan (1), J.Schmiedt (1), C. Pantelis (3), C. Basar-Eroglu

(1,2), (1) University of Bremen, Institute ofPsychology and Cognition Research, Bremen,Germany, (2) Centre for Cognitive Science,Cognium, Bremen, Germany, (3) MelbourneNeuropsychiatry Centre, Department of Psy-chiatry, The University of Melbourne andMelbourne Health, Melbourne, AustraliaChanges in the oscillatory EEG activity dur-ing recognition were assessed using a delay-dependent working memory task. Twelve sub-jects classifying stimuli as matching or non-matching during the recognition phase with atleast 90% correct were measured. Oscillatoryactivity was investigated in the delta, theta andalpha range. A late positive delta componentoccurred later for recognition of non-matchingthan matching trials, which might reflect pro-longed searching. For the theta activity a long-range integrated network of occipital, parietaland frontal sites was identified. This networkwas modulated by stimulus type (matching ver-sus non-matching) and delay. While for shortdelays recognition of matching stimuli reliedon posterior theta activity, frontal theta activ-ity was crucial for recognition after long delays.This might indicate switching between percep-tual and cognitive strategies. Similar resultswere found for alpha activity. However, alphanetworks might be additionally involved in in-creasing early sensory processing demandsfor matching the stimulus to the fading memoryduring longer delays. Taken together, thesefindings demonstrate that working memory re-lies on multiple oscillatory networks of differ-ent frequencies, which serve different func-tions necessary for recognition and are modu-lated in their timing and regional specificity de-pending on task demands.

Relationships between evoked potentials,



spontaneous EEG and intelligence mea-sures. M. Schier, C. Stough, FLSS, Swin-burne University of Technology, Melbourne,AustraliaIn our study we recorded and examined therelationship between evoked, spontaneousEEG, and a measure of intelligence. Withevoked potentials, the string length is effec-tively the length of a piece of string laid overthe normalised evoked response curve, andcaptures information about excursions of theevoked response trace, such that a largerstring length effectively means more changesor greater differences between positive andnegative changes. This has been previouslycorrelated with intelligence. With sponta-neous activity, a series of measures basedaround statistical moments (and also knownas the Hjorth parameters activity, mobility &complexity) can be derived. Of these, thecomplexity makes a measure of rapidity ofchanges. This has been previously correlatedwith string length. As previous studies havedemonstrated a relationship between stringlength (an evoked measure) and intelligence,and string length and complexity (a sponta-neous measure), the missing connection isbetween complexity and intelligence. Thisstudy is a 3-way comparison of spontaneous,evoked and intelligence measures, using theauditory evoked potential. The initial resultsare the first to show relationships betweenthese three measures and will be reportedon in this presentation. The future benefits ofthe results of this study may save time andsimplify recording parameters for analysingbrain electrical activity.

Rapid information processing revealedby electrical brain activity mapping. W.

Skrandies, Institute of Physiology, Justus-Liebig University, D-35392 Giessen, Germany

Human perception, thinking, and spontaneousmovement or reaction to stimuli occurs in thesplit-second range. Electrical brain activitymapping shows topographically distinct tem-poral components or microstatesthat occur inrapid succession. For example, simple visualstimuli yield components at 80, 100, and 120ms that reflect different brain processes.

Until a few years ago, there was a distinctionbetween so-called exogenous and endoge-nous components of event-related brain activ-ity. These were interpreted to index the pro-cessing of physical stimulus features or theinfluence of attention and cognitive process-ing. Recent publications have demonstratedthat such a distinction is not warranted. Thetopography of ERPs components occurring asearly as 100 ms after stimulus presentationis significantly influenced by attention, stimu-lus compatibility, or semantic meaning of lan-guage material. This suggests very rapid infor-mation processing of simple and complex stim-uli in primary cortical areas.

A look at basic facts from sensory physiol-ogy and neurophysiology reveals that such re-sults are far from surprising. Axonal conduc-tion velocity is very high, distances within thebrain are very small, and afferent routing tomany different brain areas occurs in parallelpathways. There are many sensory, motorand cognitive processes that occur very fast:simple stimulus perception and processing ofinformation contained in dynamic random-dotstereograms, motor reaction to simple stim-uli or regular and ëxpress saccadesäs well ashigher cognitive processing like reading (andunderstanding) words, or occur in fractions of



seconds.Thus, in combination with electrical and fMRIbrain imaging techniques, brain electrical ac-tivity mapping is an appropriate and useful toolfor investigating sensory and cognitive func-tions of the human central nervous system.

The renaissance of the electrophysiolog-ical methods in schizophrenia research.S. Galderisi, Department of Psychiatry, Uni-versity of Naples SUN, Naples, ItalyRecently, several factors contributed to the re-nascence of the electrophysiological methodsin schizophrenia research; the most influen-tial ones include: 1) the validation of previ-ously reported electrophysiological findings bymeans of functional brain imaging techniques;2) the possibility offered by electrophysiologi-cal techniques to study brain’s systems phys-iological and pathological activity with a hightemporal resolution; 3) a different conceptual-izations of psychopathological phenomena, in-creasingly regarded as a consequence of thefailure to integrate the activity of different brainareas. Main deliveries of such renascenceinclude advances in the study of abnormalfunctional connectivity underlying schizophre-nia symptoms and the identification of elec-trophysiological endophenotypes. In spite ofthe fact that electrophysiological abnormalitieswere shown to be related to diagnostic sub-types, risk factors, symptom dimensions andprognosis, electrophysiological methods arestill of limited impact in clinical settings, andtheir application is confined to the exclusion oförganic“brain pathology.

New research potential of Mismatch Nega-tivity: ”Optimized”multifeature paradigmsin clinical psychiatry. C. Norra (1), H.

Thoennessen (2), (1) Dept. of Psychiatryand Psychotherapy, Laboratory of ClinicalNeurophysiology, Ruhr University Bochum,Germany, (2) Dept. of Child and AdolescentPsychiatry and Psychotherapy, University Hos-pital Aachen /Institute of Medicine, ResearchCenter Juelich, Germany

In neurophysiology, the mismatch negativity(MMN) of evoked potentials was consis-tently used to unmask deficits in pre-attentiveinformation processing in schizophrenia -though not specific for this disorder. Tradi-tionally,studies were performed with so-calledöddballparadigms applying 10-20% of de-viants within a series of standard tones.Instead, Näätänen et al. (2004)proposed anöptimizedmultifeature design with 50% of de-viants operating 5 different deviants. Theseprocedures were primarily employed in non-clinical samples only and extended to multipleassignments.

While we aimed at comparing the two pro-cedures in EEG and MEG in schizophrenia,the optimized design was fastest to detectMMN changes. MMN was mostly reduced inschizophrenia if measured with MEG in the op-timized paradigm reaching mean effect sizesof 0.85 (max. 1.5) as opposed to 0.65 inthe traditional MMN profile recorded with EEG.Moreover, the MMNm of the left auditory cortexcorrelated significantly with positive symptomsfor schizophrenia in both paradigms (Thön-neßen et al. 2008). Especially the relation-ship of MMN deficits to psychopathology willhave to be further clarified, and our resultsare currently replicated in patient samples withchronic schizophrenia as well as ADHD andsubstance abuse (Norra et al. in prep.) How-ever, despite advantages of multifeature MMN



designs with shorter duration, higher sensi-tivity and multitude of characteristics to beanalysed it remains open whether these newMMN tools are similar to the sensory mem-ory trace build up by standard stimuli in theoddball MMN or rather reflect deficits in thecentral nervous representation of tonal char-acteristics. Therefore, minimal changes in theearly auditory processing of multiple compo-nents would also be of relevance to the hu-man speech including prosody (e.g. Kujalaet al. 2005, Pakarinen et al. 2007). Thus,further investigation of pseudowords arrangedin MMN pattern with either emotionally neu-tral or positive and negative intonation showedstronger bilateral MMNm of the latter, with pre-dominance on the right hemisphere in the tra-ditional and optimized designs in healthy in-dividuals (Thoennessen et al. 2010). Thesefindings will have implications for the early in-formation processing and detection of physicaland emotional contents of sounds, speech andsocial cognition of different psychiatric disor-ders as being studied.

Impact of EEG-vigilance on brain glucoseuptake measured with [18F]FDG-PET inpatients with depressive episode or mildcognitive impairment. T. Günther (1), P.Schönknecht (1), S. Hesse (2), S. Olbrich, C(1) . Sander (1), P. M. Meyer (2), G. Becker (2),J. Luthardt (2), U. Hegerl (1), O. Sabri (2), (1)Department of Psychiatry and Psychotherapy,University Hospital Leipzig, Leipzig, Germany;(2) Department of Nuclear Medicine, Univer-sity Hospital Leipzig, Leipzig, Germany[18F]fluorodeoxyglucose positron emissiontomography ([18F]FDG-PET) is a well-established method for the examination ofthe cerebral glucose metabolism of patients

with affective disorder or memory impairment.Building upon previous neuroimaging stud-ies, we supposed an association betweenelectroencephalogram (EEG)-vigilance andnormalized brain [18F]FDG-uptake (nFDGu)as measured by [18F]FDG-PET. For the firsttime, the present study exploratively investi-gated this association in a routine diagnosticwork-up.

Simultaneous EEG and [18F]FDG-PET underresting conditions were acquired from 14 pa-tients with depressive episode or mild cog-nitive impairment (MCI). EEG-vigilance wasautomatically classified by using the VIGALLalgorithm (Vigilance Algorithm Leipzig). Anonparametric voxelwise simple linear regres-sion with vigilance measure as predictor andnFDGu as criterion was performed using Sta-tistical nonParametric Mapping toolbox.

The main finding was a significant negativecorrelation between vigilance measure andnFDGu in bilateral frontal and temporal re-gions, bilateral cingulate gyrus and right thala-mus with vigilance-related changes of nFDGubetween 17.1 and 44.4%.

Simultaneous EEG and [18F]FDG-PET underresting conditions revealed that brain regionsassociated with EEG-vigilance partly over-lapped with regions of impaired nFDGu indepression and MCI, as reported by previousstudies. Vigilance-related changes of nFDGuwere about the same size as disease-relatedmetabolic changes in patients with affectivedisorder or memory impairment as reported inprevious studies. Therefore, our data suggestthat differences in EEG-vigilance might influ-ence alterations of nFDGu in disorders suchas depression or MCI. Whether this possibleimpact of vigilance on nFDGu should be taken



into account during the routine diagnostic ap-plication of [18F]FDG-PET has to be exploredin future studies with larger patient groups.

qEEG during trance healing: simultaneousresults from healer and client.P. L. Faber, P. Milz, F. Schlegel, D. Lehmann,The KEY Institute for Brain-Mind Research,University Hospital of Psychiatry, Zurich,SwitzerlandTwo experienced trance healers (PascalVoggenhuber and Bahar Voggenhuber-Yilmazwho occasionally treat each other) wererecorded simultaneously, each with 27 EEGchannels. During no-task resting, their powerspectra differed strongly: BV-Y showed analpha power peak at 8.5 Hz, PV at 11.5 Hz.The two participants alternated their functionsas trance healer and as client (8 sessions of15 min: each participant 4 times as healer,4 times as client). FFT spectral analysis wasdone using average reference. Spectra wereaveraged across the 27 channels. Powervalues were integrated for each of the eightfrequency bands from delta through gamma.Resting states differed significantly from heal-ing and client states. The eight simultaneousresults of the healing sessions were statisti-cally compared (band-wise block ANOVA). Intheir function as trance healer, both partici-pants showed significantly less power in thedelta and beta-3 EEG frequency bands than intheir function as client. In sum, this pilot studyof trance healing produced distinct qEEGstates (that combined EEG characteristics offunctional inhibition and functional facilitation)in healer and client that cannot be reduced tochanges towards drowsiness or alertness.

EEG individual alpha frequency linked to

functional and structural MRI. K. Jann, A.Federspiel, M. Kottlow, T. Dierks, T. Koenig,(1) Department of Psychiatric Neurophysiol-ogy, University Hospital of Psychiatry, Univer-sity of Bern, Bern, SwitzerlandIn this study we tried to find functional andstructrural differences related to subjects in-dividual alpha frequencies (IAF). IAF variesacross subjects and is associated to a per-sons cognitive capabilities, especially in work-ing memory processes. For this purposewe recorded simulatneous EEG-fMRI and dif-fusion tensor images (DTI). Functionally, wefound that small intra-indiviudal temporal IAFfluctuations are positively related to increasedBOLD signal in brain aras involved in work-ing memory functions and the modulation ofattention. Structural differences dependingon interindividual IAF differences were foundin fascicles connecting the above mentionednetworks: subjects with higher IAF show in-creased DTI functional anisotropy (FA) values.These two observations taken together sug-gest that it is plausible that increased IAF im-proves task performance because there is in-creased activity and better connectivity in therelevant functional networks.

Analysis of ERP-data with matrix-waveletsand PCA. A. Klein (1), T. Sauer (1), W.Skrandies (2), Department of Mathematics,(2) Institute of Physiology, Justus-Liebig Uni-versity, Giessen, GermanyWhenever data from an array of EEG-electrodes is processed, the modelling ofdependencies between electrodes tends tocomplicate the processing of the data signifi-cantly when each channel is processed sep-arately as a scalar time-series. In this case,every pair of electrodes has to be handled



separately which becomes very cumbersome,even for moderate numbers of channels, sincethe number of pairs grows quadratically withthe number of channels. This problem isremedied somewhat when the ensemble ofchannels is viewed as a multidimensionaltime-series that allows the dependencies tobe modelled in the form of matrices operatingon the time series via matrix-vector products,for example. However, a few things still remainto be considered: Time delays between chan-nels cannot be modelled this way, as well asa number of more general dependencies thatare not necessarily useful for EEG-analysis,but would be interesting in other settings. Asa first step towards a general framework formultidimensional data analysis, we appliedthe novel method of matrix-wavelet-analysis tohuman SEP-data. The results of the matrix-wavelet-transform, which are complex-valuedin this case, were further processed with prin-cipal component analysis, allowing us to testfor:

1. Variations in the dimensionality of thedata,

2. Shifting of spatial centroids of activity forcertain components under different condi-tions,

3. Shifting of centroids of activity in time-frequency-space for certain componentsunder different conditions.

The results were compared with the resultsthat will be achieved when each channel issubjected to the scalar wavelet transform withPCA only applied to the aggregated trans-forms.

Print tuning during fast reading: a simul-taneous EEG-fMRI study. J. Kronschnabel(1), U. Maurer (1), R. Schmid (1), D. Brandeis(1,2), (1) Department of Child and AdolescentPsychiatry, University of Zürich, Switzerland,(2) Department of Child and Adolescent Psy-chiatry and Psychotherapy, Central Institute ofMental Health, Mannheim, Germany

Tuning of visual activity for print yields an in-creased occipito-temporal N1 at about 150-250 ms in the event-related potential (ERP) towords compared to symbol strings. In func-tional Magnetic Resonance Imaging (fMRI) acorresponding specialization has been locatedin an occipito-temporal visual word form (VWF)system. In developmental studies specializa-tion for print was reduced in adults comparedto beginning readers. Yet, this was underslow presentation conditions that did not chal-lenge adult reading skills adequately. Here, wetest whether specialization for print increases ifstimuli are presented under faster, more chal-lenging conditions.

Words and symbol strings were presented to 8adults for either 700 or 100 ms (long vs. shortcondition), while keeping SOA constant (1950ms). ERP (59 channels) and fMRI data werecollected simultaneously in a 3T scanner us-ing a block design. Preliminary analyses re-vealed a larger left occipito-temporal N1 forwords than for symbols, and a reversed pat-tern over the corresponding right hemispherein both the short and long conditions. Thistuning effect, however, was not further mod-ulated by the presentation duration. Althoughthe fMRI random effects analysis showed theexpected activation pattern for the word andsymbol conditions, no robust word-symbol dif-ferences emerged in VWF regions neither with



long nor with short presentation duration.In conclusion, robust N1 effects indicating spe-cialization for print could be obtained fromthe simultaneous recordings suggesting suc-cessful removal of scanner-related artifacts.Shorter presentations that challenge the read-ing system more strongly did not increase N1print tuning in a sample of normally readingadults. The absence of any word-specific VWFactivation in the fMRI data may be due to thesmall sample size, as previous studies usinglarger samples have found such effects to beweak. Alternatively, short presentations alonemay not sufficiently challenge the mature read-ing system.Supported by the Swiss National Science Founda-

tion.

Functional sLORETA tomography of EEGduring hypnotic and voluntary arm lifting.D. Lehmann (1), E. Cardeña (2), P. L. Faber(1), P. Jönsson (2), P. Milz (1), R. D. Pascual-Marqui (1), K. Kochi (1), (1) The KEY Institutefor Brain-Mind Research, University Hospital ofPsychiatry, Zurich, Switzerland, (2) Center forResearch on Consciousness and AnomalousPsychology (CERCAP), Lund University, Swe-denWhat is the brain electric mechanism of hyp-nosis? The comparison of voluntary motoracts and motor acts under hypnosis can beused to compare hypnotic versus non-hypnoticbrain states. In an earlier pilot study on foursubjects [1], the dipole model source of thedelta-theta (inhibitory) EEG frequency bandwas more posterior and the source of the al-pha (routine function) and beta (facilitatory)bands was more anterior during hypnotic com-pared to voluntary arm lifting. - The presentrepeat study tested these findings in 30 volun-

teers (10 high, 10 medium, 10 low hypnotiz-ables), applying sLORETA functional tomogra-phy analysis. As in the earlier study, only leftarm movements were done (as is common inhypnosis studies as right hemisphere functionsare apparently more amenable to hypnotic in-fluence). Stronger in the hypnotic than vol-untary condition was left prefrontal facilitatoryactivity and left central-superior temporal in-hibitory activity, weaker was left inferior frontal-superior temporal inhibitory activity and rightpostcentral-temporo-parietal facilitatory activ-ity. Results were similar over hypnotizabiltygroups. - These results confirmed our earlierstudy, showing anterior facilitation and poste-rior inhibition in the hypnotic condition, and theopposite in the voluntary condition. Increaseof self-rated hypnotic depth correlated with in-creased anterior inhibitory and decreased cen-tral facilitatory activity in the left hemisphere.Since only left arm data were available, the fullrole of the hemispheres remains to be clari-fied in future work. Reference: [1] Lehmann,D., Faber, P.L., Isotani, T. and Wohlgemuth,P. Source locations of EEG frequency bandsduring hypnotic arm levitation: a pilot study.Contemporary Hypnosis 18: 120-127 (2001).Erratum in: Contemporary Hypnosis 18: 220(2001).Supported in part by Bial Foundation

Preliminary tomographic neurofeedbackresults from children with ADHD. S. Mau-rizio (1), M. Liechti (1,2), H. Heinrich (3),G. Thalmann (1), L. Meier(1), Y. Schwitter(1), S.Hossmann (1), S. Walitza (1), H.-C.Steinhausen (5), L. Jäncke (2), R. Drechsler(1), D. Brandeis (1,6), (1) Dept. of Child andAdolescent Psychiatry, University of Zürich,Switzerland; (2) Dept. of Neuropsychology,



Institute for Psychology, University of Zürich,Switzerland; (3) Dept. of Child and AdolescentPsychiatry, University of Erlangen-Nürnbergand Heckscher-Klinikum, München, Germany;(4) Dept of Child and Adolescent Psychiatry,University of Leipzig, Germany; (5) AalborgPsychiatric Hospital, Aarhus University Hos-pital, Aalborg, Denmark; (6) Dept. of Childand Adolescent Psychiatry and Psychother-apy, CIMH, University Heidelberg-Mannheim,Germany; and CIHP, University of Zürich,Switzerland

In this ongoing study, electroencephalogram(EEG) based tomographic neurofeedback(tNFB) is evaluated and compared to an EMGbiofeedback training to clarify specific andnonspecific contributions to the treatment ofattention deficit hyperactivity disorder (ADHD)in children. We hypothesised that region spe-cific tNFB training leads to increased contin-gent negative variation (CNV; an event-relatedpotential component reflecting preparation).A group of 13 children with ADHD (8.5-13y)was trained over 18 sessions to regulatetheir theta/beta-frequencies and slow corti-cal potentials (SCP) in the anterior cingulum(ACC). Thirty-one-channel EEG was usedto calculate low-resolution electromagnetictomographic (sLORETA) NFB. CNV changeswere recorded as pre-/post-measurement in acued continuous performance test (CPT).

Following tNFB training, we found improve-ment on behavioural rating scales and atendency toward normalisation of the CNV.What aspects of regulation improved withtNFB training is currently being analyzed.Analyses of the EMG control group are alsounder way. Group comparisons will furtherclarify how specific this tomographic technique

is.Supported by the SBF COST B27 ENOC and by a

grant to the GD, Kanton Zurich

EEG power and synchronization is differ-ently linked to the BOLD signal in chil-dren and adults during working memory.L. Michels (1), R.Lüchinger (2), T. Koenig (3),E. Martin (1,4), D. Brandeis (2,4,5), (1) MR-Center, University Children’s Hospital, Univer-sity of Zurich, Zurich, Switzerland; (2) Depart-ment of Child and Adolescent Psychiatry, Uni-versity of Zurich, Zurich, Switzerland; (3) De-partment of Psychiatric Neurophysiology, Uni-versity Hospital of Psychiatry, Bern, Switzer-land; (4) Center for Integrative Human Physiol-ogy, University of Zurich, Zurich, Switzerland;(5) Department of Child and Adolescent Psy-chiatry and Psychotherapy, Central Institute ofMental Health, Mannheim, GermanyIncreased theta band (4-7 Hz) activity ispresent typically when children and youngadults performing a cognitively demandingtask. Theta rhythms have been recently in-vestigated in adults during short-term workingmemory (STWM) by simultaneous EEG-fMRIrecordings, revealing an inverse relation tothe BOLD (blood oxygen level dependent)signal. Yet, not only spectral power but alsosynchronization plays a fundamental role incognitive processing, since the level of thetaband synchronization is modulated duringSTWM. However, little is known about poten-tial interactions between the BOLD signal andEEG synchronization during STWM. Further,it is unclear whether EEG-BOLD signal cor-relations differ between adults and children.In addition, the link between behaviour andphysiological markers (i.e., power, synchro-nization, and the BOLD signal) during STWM



is not fully understood yet. In this study weasked in 18 young adults and 15 childrenwhether EEG-BOLD signal correlations showage-dependent effects during a SternbergSTWM task. Our results reveal that frontalEEG theta power and theta-BOLD signalcorrelations were significantly enhanced inchildren compared to adults, i.e. the latterbeing visible as negative theta-BOLD signalcorrelations. In contrast, correlations betweentheta synchronization and the BOLD signalwere exclusively positive but only significant(p < 0.001, uncorrected) in adults at midlinefrontal regions, right posterior parietal cortex,and posterior cingulate cortex. Synchroniza-tion but not power correlated positively withperformance during the most demanding loadcondition in both groups of subjects, however,significantly stronger in the adults. Our resultsindicate that theta EEG-BOLD signal corre-lations depend differently on spectral powerand synchronization and that they show age-dependent effects. Specifically, the weakertheta EEG and theta-BOLD signal synchro-nization effects in children might indicatenot fully developed cognitive processing. Thisseems to be supported by the weaker couplingbetween synchronization and performance inchildren compared to adults.

Response control in patients with border-line personality disorder. M. Ruchsow (1),J. Karitzky (1), G. Grön (2), D. Brummer (2),M. Falkenstein (3), L. Hermle (1), (1) Dept. ofPsychiatry Christophsbad, Faurndauer Str. 6-28, D-73035 Göppingen, Germany; (2) Dept.of Psychiatry, University of Ulm, Leimgruben-weg 12-14, D-89075 Ulm, Germany; (3) Leib-niz Research Centre for Working Environmentand Human Factors (IfADo), Ardeystr. 67, D-

44139 Dortmund, GermanyNogo-N2 and Nogo-P3 are supposed to beelectrophysiological correlates of responsecontrol. Both ERP-components were mea-sured in patients with borderline personalitydisorder (BPD, n = 17) and an independentsex-, age-, and education-matched controlgroup.Participants performed a hybrid flanker-Go/Nogo paradigm while a 64-channel EEGwas recorded.BPD patients showed reduced Nogo-P3 am-plitudes compared to healthy controls; with re-spect to the Nogo-N2 there were no significantgroup differences. Possibly, the Nogo-P3 canbe used as an electrophysiological marker in-dicating increased levels of impulsiveness. Anadditional study with healthy controls supportsthis view. Further research is needed to ex-actly determine the underlying neuropsycho-logical and neurobiological mechanisms re-sulting in altered Nogo-P3 amplitudes in psy-chiatric patients.

Response control in patients withobsessive-compulsive disorder.M. Ruchsow (1), J. Karitzky (1), G. Grön (2),D. Brummer (2), M. Falkenstein (3), L. Hermle(1), (1) Dept. of Psychiatry Christophsbad,Faurndauer Str. 6-28, D-73035 Göppingen,Germany; (2) Dept. of Psychiatry, Univer-sity of Ulm, Leimgrubenweg 12-14, D-89075Ulm, Germany; (3) Leibniz Research Centrefor Working Environment and Human Factors(IfADo), Ardeystr. 67, D-44139 Dortmund,GermanyNogo-N2 and Nogo-P3 are supposed to beelectrophysiological correlates of responsecontrol. Both ERP-components were mea-sured in patients with obsessive-compulsive



disorder (OCD, n = 13) and an independentsex-, age-, and education-matched controlgroup.Participants performed a hybrid flanker-Go/Nogo paradigm while a 64-channel EEGwas recorded.OCD patients showed enhanced Nogo-N2 am-plitudes compared to healthy controls; with re-spect to the Nogo-P3 there were no significantgroup differences. Possibly, the Nogo-N2 canbe used as an electrophysiological marker indi-cating increased levels of compulsiveness. Anadditional study with healthy controls supportsthis view. Further research is needed to ex-actly determine the underlying neuropsycho-logical and neurobiological mechanisms re-sulting in altered Nogo-N2 amplitudes in psy-chiatric patients.

The syntax of EEG microstates issequence-inverted in skeptics and believ-ers of paranormal phenomena. F. Schlegel,D. Lehmann, P. Faber, P. Milz, K. Kochi, TheKEY Institute for Brain-Mind Research, Uni-versity Hospital of Psychiatry, ZurichBelievers in paranormal phenomena havebeen hypothesized to have an increased vul-nerability for schizophrenia. We tested thiscontention using microstate syntax analysis.The participants were selected from volunteeruniversity students using a self-report scalefor paranormal beliefs and experiences. Spon-taneous brain electric activity (multichannelEEG) of believers (n=16) and skeptics (n=13)was recorded during closed eyes resting. EEGviewed as series of momentary potential distri-bution maps (’landscapes’) can be parsed intosegments of quasi-stable landscape, the mi-crostates, the putative ’atoms of thought’ thatlast about 100 ms. The microstates that were

obtained from the present data were clus-tered into four microstate classes (A,B,C,D;Koenig et al., NeuroImage, 2002) that repre-sent different types of information processing.Analysis of the temporal sequence (syntax)of these microstate classes revealed that be-lievers showed a predominant sequence ofmicrostate concatenations from A to C to B toA that was reversed in skeptics (A to B to C toA). - The present study demonstrated that sub-clinical differences in personality can be de-tected in resting EEG microstate syntax. Themicrostate concatenation sequences reportedin a previous study that examined microstatesyntax in medication-naive schizophrenics(Lehmann et al., Psychiatry Res, 2005) do notagree with the present results for believers. Insum, the studies did not reveal similarities inEEG microstate syntax between believers inparanormal phenomena and schizophrenics.

Aging, inhibiton measured by ERPs and in-traindividual variability. C. Schmiedt-Fehr,S. Dühl, C. Basar-Eroglu, Institute of Psy-chology and Cognition Research, University ofBremen, GermanyERPs are a valuable and common tool forstudying changes of inhibitory function withage. This approach is based on the hypothe-ses that the detected signal in each single trialhas stable characteristics, such as constantwaveform morphology, amplitude, latency andspectral composition across all trials. Con-sidering evidence for increased intraindividualvariability (short-term trial-to-trial fluctuation)of behavior in later adulthood this assumptionmay not be unproblematic when applied to re-search in the field of cognitive aging. Thepresent study aimed at verifying previously re-ported ERP results on inhibition-related sub-



processes in auditory and visual modality insingle trial analysis. Commonly estimated Go-and NoGo ERP (N2/P3) components ampli-tude and latencies measures were comparedwith single trial estimations of time frequencymagnitude and inter trial phase-locking in thedelta and theta frequency range. In the au-ditory modality the single trial analysis mainlysupported the previously reported ERP re-sults, indicating inhibition-related changes withage in the P3 time range. In the visual modal-ity main results also supported earlier ERP re-ports. In addition the results suggest that es-pecially theta oscillations may be associatedwith age-related changes in response inhibi-tion. The comparison of both the ERP and sin-gle trial time-frequency approach did not sup-port the hypotheses that older age is relatedto increasing intraindividual variability in neu-ral responses, at least during Go and NoGoprocessing.

Reliability of the STROOP interferencetask: An ERP study. T. Fehr(1,2), J. Wiechert(1), M. Herrmann (1,2), (1) Dept. of Neuropsy-chology/Behavioral Neurobiology, Center forCognitive Sciences, University of Bremen,Bremen, Germany; (2) Center for AdvancedImaging Bremen/Magdeburg, Bremen, Ger-manyThe STROOP-paradigm is one of the mostconsistent experimental approaches in psy-chological sciences. However, retest-reliabilityin individual physiological parameters has notbeen examined in both experimental intra- andinter-session arrangements. Based on previ-ously published data, we applied an adaptedform of the STROOP-task in an EEG-study toestimate individual intra- and inter-session re-liability of behavioural and electrophysiologi-

cal data. Behavioural data showed both con-sistent split-half as well as re-test reliability in15 healthy young female study participants.There was an expected interference effect inthe incongruent condition reflected in longerresponse times compared to both congruentand baseline conditions, and a facilitation ef-fect in the congruent condition reflected inshorter response times compared to the base-line condition. Behavioural data will be dis-cussed in relation to the respective electro-physiological findings.

The feeling of colors - semantic dimen-sions and topography of brain electrical ac-tivity. W. Skrandies, B. Rahimi, Institute ofPhysiology, Justus-Liebig University, D-35392Giessen, GermanyThe semantic differential technique is usedin order to define dimensions of connotativemeaning. We investigated the affective mean-ing of color words. 13 different words wererated on adjective scales of opposite meaningby a total of 1865 healthy young adults. Wefound three dimensions that reflected ”evalua-tion” (E, friendly, good, nice, etc.), ”potency” (P,strong, big, heavy, etc.), and ”activity” (A, fast,noisy, lively). Different colors had different fac-tor scores that were used to classify colors insix different classes (E+/E-, P+/P-, A+/A-).During ERP recordings, color words were pre-sented in random order on a monitor. Attentionwas controlled by instructing subjects to couldunrelated words appearing at random inter-vals. EEG was recorded from 42 healthy adultsfrom 30 channels between the inion and Fz.ERPs were computed offline according to stim-ulus class. Repeated measurement ANOVAswere used for comparing experimental condi-tions.



Between 70 and 410 ms latency five com-ponents were identified by the occurrenceof maximal Global Field Power (GFP). Be-tween 70 and 130 ms different semanticclasses yielded significantly different GFP(F(2,82)=29.97; p<.00001): colors judged as”active” or ”passive” (yellow / orange or brown /black) were followed by high GFP while colorsrelated to potency (P) showed smallest re-sponse amplitudes (red / gold or pink / silver).A very similar effect was seen between 130and 190 ms (F(2,82)=22.48; p<.00001). Thiscomponent displayed significantly differentlatencies (F(2,82)=5.72; p<.0047) where colorwords related to activity (A) had smallest la-tencies. In addition, there occurred a numberof significant topographical effects. Our resultsshow that color words can be consistentlyclassified according to their connotative, affec-tive meaning. Such differences are reflectedby ERP components occurring after about100 ms latency when color words are read byhealthy adults.


Book Review

W. Skrandies – ElectricalNeuroimaging (Book Review)

W. Skrandies, Institute of Physiology,Justus-Liebig University, D-35392 Giessen,

[email protected]

This book is a tutorial text written by a groupof ten experienced scientists who work in thefield of multichannel EEG since a long time.The basis for ”Electrical Neuroimaging” of hu-man brain activity is the topographical analy-sis of brain electrical activity recorded from thesurface of the head. A strictly topographicalapproach to the assessment of the electricalfields of the brain allows the dynamic mappingof functions of the central nervous system inboth healthy subjects and patients with neuro-logical or psychiatric symptoms.

The individual chapters aim at an overviewof the neurophysiological basis for electricalimaging (see Chapter 1: “From neuronal ac-tivity to scalp potential fields”) and on method-ological questions of recording and data anal-ysis. The reader also learns about practi-cal problems with data acquisition and pre-processing, and the basic analysis of the elec-trical fields of the brain. The most instructivechapters explain the statistical analysis of mul-tichannel scalp field data, neuroimaging in thetime domain as well as methods of multichan-nel frequency and time-frequency analysis. Inaddition, source localization approaches andthe imaging of the underlying neuronal gener-ators of EEG (and MEG) are presented in de-tail. The last chapter gives an outlook on futuredevelopments and the integration of EEG withother functional brain imaging methods.

In this book, scientists in the field as wellas experienced EEG-readers will learn aboutthe quantitative and statistical spatio-temporalanalysis of multichannel-recorded head sur-face potential fieldsThere are only a few (formal) shortcomingsthat can be easily corrected in a future editionof the book. As in many review publications,the cited literature is somewhat selective, andit contains a few errors. These are small short-comings. However, there is no author index;this makes it impossible to search for individualcontributors to the scientific literature. Most fig-ures are clear and instructive, but some of thefigures are very small, and in some instancesthe choice of color appears unfortunate.In summary, this book enables researchersto apply appropriate analysis strategies tomultichannel EEG data. This also helpsto avoid mistakes when analyzing and in-terpreting head surface recorded electricalmeasurements. The book also contains de-tailed descriptions of the analysis proceduresdiscussed. I trust that this volume can becomean authoritative reference that gives a system-atic overview of the theoretical and practicalpossibilities offered by a strictly topographicalanalysis of EEG and ERP data.

Electrical Neuroimaging. Edited by C. M. Michel,T. Koenig, D. Brandeis, L. R. R. Gianotti & J. Wack-ermann. Cambridge University Press, 2009, ISBN-13: 9780521879798, £ 70.00 / 85.40 / US$ 125.-


Announcements — Ankündigungen

Announcements — Ankündigungen

• ISBET Meeting

The annual meeting of the International Society for Brain Electromagnetic Topography (ISBET) willtake place in Heidelberg, Germany, as a Joint Meeting of ISBET / ISNIP / ECNS from September 7to 10, 2011.

Information and Registration at: http://www.isnip2011.unitt.de

• ISBET Workshop on Topographical Analysis of EEG/ERP Data (T. Koenig & W.Skrandies)

This workshop will take place during the Joint Meeting of ISBET / ISNIP / ECNS. It willexplain the basics of topographical analysis. We will first outline the intrinsic relation be-tween brain electric sources and scalp field measurement. Then, we introduce the possiblemethods quantify and compare scalp fields, to define components topographically, and todo subsequent statistical comparison. In the first part we will illustrate the theoretical basesof topographical analysis; for the second part it is planned to present a practical demon-stration of analysis steps by the application of analysis software.

• 20. Deutsches EEG/EP Mapping Meeting / 20th German EEG/EP Mapping Meeting

Conference language is German; English contributions will be accepted.

– 14. bis 16. Oktober 2011; Schloss Rauischholzhausen

– Schwerpunkte / Themen

∗ H.-R. Duncker (Gießen) Die Entwicklung der Menschen zu Sprach- und Kultur-wesen

∗ M. Ruchsow (Göppingen) Personale Identität aus Sicht der Neurowissenschaftenund der (analytischen) Philosophie

∗ M. Doppelmayr (Salzburg) Symposium über Neurokognitive Prozesse im Sport“

∗ T. Fehr (Bremen) Symposium über Ëlektrophysiologie und Interferenzprozesse:Dynamik, Individualität und Stabilität“

– Anmeldeschluss ist der 14. August 2011

– Information und Anmeldung unter: http://www.med.uni-giessen.de/physio/


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