(Time )Frequency Analysis of EEG Waveforms - …

1 ( time ) frequency Analysis of EEG WaveformsNiko BuschCharit e University Medicine Berlin; Berlin School of Mind and / 23 From ERP Waveforms to wavesERP Analysis : time domain Analysis : when do things (amplitudes) happen?treats peaks and troughs as single domain (spectral) Analysis (Fourier Analysis ):magnitudes and frequencies of waves no time and troughs are not treated as separate frequency Analysis (wavelet Analysis ):when do which frequencies / 23 From ERP Waveforms to wavesERP Analysis : time domain Analysis : when do things (amplitudes) happen?treats peaks and troughs as single domain (spectral) Analysis (Fourier Analysis ):magnitudes and frequencies of waves no time and troughs are not treated as separate frequency Analysis (wavelet Analysis ):when do which frequencies / 23 From ERP Waveforms to wavesERP Analysis : time domain Analysis : when do things (amplitudes) happen?

2 Treats peaks and troughs as single domain (spectral) Analysis (Fourier Analysis ):magnitudes and frequencies of waves no time and troughs are not treated as separate frequency Analysis (wavelet Analysis ):when do which frequencies / 23 Why bother?( time ) frequency Analysis complements signal Analysis :neurons are of signals with trial-to-trial of longer time of pre-stimulus and spontaneous for sophisticated methods (coherence, coupling, causality, / 23 Parameters of wavesOscillations regular repetition of some measure over several length of a single cycle ( period).Frequency1wavelength the speed of current state of the oscillation angle on the unit circle. Runsfrom 0 (- ) 360 ( )Magnitude (permanent) strength of the / 23 How to disentangle oscillationsJean Joseph Fourier (1768 1830): An arbitrary function, continuous or withdiscontinuities, defined in a finite interval by an arbitrarily capricious graph canalways be expressed as a sum of sinusoids / 23 The discrete Fourier transformThe DFT transforms the signal from the time domain into the that the signal be 5055 50550 50510 505 Sum of 5 + 10 + 50 Time050100024 FFT SpectrumHz050100012 FFT SpectrumHz050100024 FFT / 23 The discrete Fourier transformThe DFT transforms the signal from the time domain into the that the signal be 100 50050100 EEG raw dataTime [sec]01234 100 50050100reverted raw dataTime [sec]020406005101520 FFT SpectrumHz020406005101520 FFT / 23 The discrete Fourier transformThe DFT transforms the signal from the time domain into the that the signal be signals:When does the 10 Hz oscillation occur?)

3 DFT does not give time information is not necessary for stationary signalsFrequency contents do not change all frequency components exist all to investigate event related spectral changes in brain / 23 Event related synchronisation / desynchronisationCut the signal in two time windows and assume stationarity in each power baseline powerbaseline power 100 But why not use even smaller windows? Windowed FFT / Short term Fourier & Lopes da Silva (1999). Clin / 23 The short term Fourier transform (STFT) IAssume that some portion of a non stationary signal is parameters:window function ( hamming , Hanning, Rectangular, etc.)window overlapwindow length: width should correspond to the segment of the signal where itsstationarity is Hanning windowHamming windowBoxcar / 23 The short term Fourier transform (STFT) IAssume that some portion of a non stationary signal is parameters:window function ( hamming , Hanning, Rectangular, etc.)

4 Window overlapwindow length: width should correspond to the segment of the signal where itsstationarity is 1000100 EEG raw Hanning window010002000300040005000600070008000 50050windowed EEG / 23 The short term Fourier transform (STFT) IAssume that some portion of a non stationary signal is parameters:window function ( hamming , Hanning, Rectangular, etc.)window overlapwindow length: width should correspond to the segment of the signal where itsstationarity is 100 50050100 EEG raw dataTime [sec]timefrequencySPECTROGRAM, R = / 23 The short term Fourier transform (STFT) IIWindow length affects resolution in time and frequencyshort window: good time resolution, poor frequency window: good frequency resolution, poor time 1000100 EEG raw dataTime [sec]frequencySPECTROGRAM, width = 1024024681012140102030timefrequencySPECT ROGRAM, width = / 23 Uncertainty principleWerner Heisenberg (1901 1976):Energy and location of a particle cannot be both known with infinite result of the wave properties of particles (not the measurement).

5 Applies also to time frequency Analysis :We cannot know what spectral component exists at any given time spectral components exist at any given interval of time ?Spectral/temporal resolution trade off cannot be avoided but it can frequency resolution at low time resolution at high / 23 From STFT to waveletsSTFT: fixed temporal & spectral resolutionAnalysis of high frequencies insufficient temporal of low frequencies insufficient spectral Analysis : Analysis of high frequencies narrow time window for better time of low frequencies wide time window for better spectral / 23 What is a wavelet?Motherwavelet t2/2 2 1 |ej 0t| | (t)|Zero mean wavelet: prototype function (f= sampling frequency ).Wavelets can be scaled (compressed) and / 23 What is a wavelet?Motherwavelet0 ( Hz )Spectral Density40 Hz10 Hz20 HzTime (s) mean wavelet: prototype function (f= sampling frequency ).

6 Wavelets can be scaled (compressed) and / 23 Wavelet transform of VWavelet transformed ERP VOzBandpass filtered ERP VOzGamma Band: ca. 30 80 [uV] [s] [Hz].. but be careful:any signal can be represented as oscillations w. time - frequency analysisbut it does not imply that the signal is / 23 Important parameters of a wavelet-0,15 -0,10 -0,05 0,000,050,100,15-0,06-0,04-0,020,000,020 ,040,060,08 AmplitudeTime[s]AWavelet - time domain0 10203040506070800,0000,0020,0040,0060,00 8 frequency (Hz)AmplitudeBWavelet - frequency domainLength how many cycles does a wavelet have? 40 Hz wavelet (25 ms/cycle), 12 cycles 250 ms length tstandard deviation in time domain: t=m2 f0 fstandard deviation in frequency domain: f=12 ttime resolution increases with frequency , whereas frequencyresolution decreases with / 23 Evoked and induced oscillations IAveragems21evoked/ phase-lockedinduced/ 200300400 500 600 700 Evoked time - frequency representation of the average of all trials (ERP).

7 Induced average of time - frequency transforms of single / 23 Evoked and induced oscillations IIWavelet Analysis of single trials reveals non phase locked phase-lockedInduced/ transformed trials-Evoked time - frequency representation of the average of all trials (ERP).Induced average of time - frequency transforms of single / 23 Phase locking factor (PLF) intertrial coherence (ITC) or phase locking value (PLV).measures phase consistency of a frequency at a particular time across = 1: perfect phase = 0: random phase / 23 The EEG state spaceFrequency x phase locking x amplitude changes2 Evoked and induced activity are extremes on a cover only small part of the EEG , Debener, Onton, Delorme (2004). / 23 Examples 1: spontaneous EEGS timulus pairs are presented at different phases of the alpha rhythm sequential or simultaneous?3If the stimulus pair falls within the same alpha cycle perceived the visual system take snapshots at a rate of 10 Hz?

8 Simultaneity and the alpha rhythmFigure from VanRullen & Koch (2003): Is perception discrete of continuous? TICS3 Varela et al. (1981): Perceptual framing and cortical alpha / 23 Examples 2: pre-stimulus EEG powerSpatial attention to left or alpha power over ipsilateral : ipsi- vs. [p]-4-2024frequency [Hz] time [s]8 15 0 s4 Busch & VanRullen (2010): Spontaneous EEG oscillations reveal periodic samplingof visual attention. / 23 Examples 3: Analysis of long time intervalsSternberg memory task with different set power increases linearly with set of set size5 Jensen et al. (2002): Oscillations in the alpha band (9 12 Hz) increase withmemory load during retention in a short-term memory task. Cereb / 23 Recommended readingWWW:EEGLAB s time - frequency functions explained: explained: tutorial polikar/ :Barbara Burke Hubbard: The World According to Smith: The Scientist & Engineer s Guide to Digital Signal Processing( ).

9 Herrmann, Grigutsch & Busch: EEG oscillations and wavelet Analysis . In:Event-related Potentials: A Methods :Tallon-Baudry & Bertrand (1999) Oscillatory gamma activity in humans and its rolein object representation. , Bopardikar, Rao & Swartz (1999) Wavelet Analysis of neuroelectricwaveforms: a conceptual tutorial. Brain / 23 Thank for your interest !Please ask / 23