(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).)

3 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?

4 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.)

5 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).

6 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?

7 Motherwavelet0 ( Hz )Spectral Density40 Hz10 Hz20 HzTime (s) mean wavelet: prototype function (f= sampling frequency ).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).

8 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?

9 3If the stimulus pair falls within the same alpha cycle perceived the visual system take snapshots at a rate of 10 Hz?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.

10 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( ).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