Time-Frequency analysis of biophysical time series

Transcription

1 Time-Frequency analysis of biophysical time series Sept 9 th 2010, NCTU, Taiwan Arnaud Delorme

2 Frequency analysis synchronicity of cell excitation determines amplitude and rhythm of the EEG signal Hz Gamma Hz Beta 9-11 Hz Alpha 4-7 Hz Theta Hz Delta 1 second

3 Frequency analysis Beta Alpha Theta Delta Low Delta

4 Stationary signals 2 Hz 10 Hz Magnitude Magnitude Time 20 Hz Magnitude Magnitude Time Hz Time Time Slide courtesy of Petros Xanthopoulos, Univ. of Florida

5 Stationary signal 2 Hz + 10 Hz + 20Hz Power spectrum Stationary Magnitude Magnitude Time Frequency (Hz) By looking at the Power spectrum of the signal we can recognize three frequency Components (at 2,10,20Hz respectively). Slide courtesy of Petros Xanthopoulos, Univ. of Florida

6 EEG amplitude Time Sinusoid Gaussian Tapered sinusoid * Performing Fourier transform by using a time moving window

7 Spectral phase and amplitude Imaginary Real Imag. Real F k (f,t)

8 Spectral phase and amplitude Imaginary Real Imag. Real F k (f,t)

9 Discrete Fourrier Transform function function X = dft(x) Loop on frequency [N,M] = size(x); n = 0:N-1; for k=n X(k+1) = exp(-j*2*pi*k*n/n)*x; end Multiply with signal Imaginary part Sine component Real part Cosine component

10 Average of squared absolute values

11 Spectral power 0 Hz 10 Hz 20 Hz 30 Hz 40 Hz 50 Hz Average of squared amplitude Power (db) Frequency (Hz)

12 Overlap 50% Average of squared amplitudes

13 padding

14 Spectrogram or ERSP 5 Hz 0 ms 10 ms 20 ms 30 ms 40 ms 50 ms 60 ms 10 Hz 20 Hz 30 Hz

15 Spectrogram or ERSP 5 Hz 0 ms 10 ms 20 ms 30 ms 40 ms 50 ms 60 ms 10 Hz 20 Hz Average of squared values 30 Hz 5 Hz 10 Hz 20 Hz 30 Hz 0 ms 10 ms 20 ms 30 ms 40 ms 50 ms 60 ms

16 Power spectrum and event-related spectral perturbation Complex number Scaled to db 10Log 10 (ERSP)

17 Absolute versus relative power Absolute = ERS Relative = ERSP (db or %)

18 Difference between FFT and wavelets FFT Wavelet Frequency

19 Wavelets factor Wavelet (0)= FFT Wavelet (1) 1Hz 2Hz 4Hz 6Hz 8Hz 10Hz

20 Time-frequency resolution trade off

21 FFT In between Pure wavelet

22 The Uncertainty Principle A signal cannot be localized arbitrarily well both in time/ position and in frequency/ momentum. There exists a lower bound to the Heisenberg s product: Δt Δf 1/(4π) Δf = 1Hz, Δt = 80 msec or Δf = 2Hz, Δt = 40 msec

23 Modified wavelets Wavelet (0.8) Wavelet (0.5) Wavelet (0.2)

24 Inter trial coherence Trial 1 Trial 2 Trial 3 same time, different trials amplitude 0.5 phase 0 amplitude 1 phase 90 amplitude 0.25 phase 180 POWER = mean(amplitudes 2 ) 0.44 or 8.3 db COHERENCE = mean(phase vector) Norm 0.33

25 Slide courtesy of Stefan Debener

26 Phase ITC Normalized (no amplitude information)

27 Power and inter trial coherence 5 Attend left-stim left Attend left-stim right db Difference ITC: trials synchronization

28 Plot IC ERSP

29 Mask IC ERSP Pure green denotes non-significant points 0.01

30 Plot IC ERSP padratio = 1 padratio = 2 Increase # freq bins

31 Plot IC ITC Shows the actual dominant phase of the signal plotphase, on

32 To visualize both low and high frequencies freqs = exp(linspace(log(1.5), log(100), 65)); cycles = [ linspace(1, 8, 47) ones(1,18)*8 ]; Cycles Frequencies

33 Component time-frequency

34 Cross-coherence amplitude and phase 2 components, comparison on the same trials Trial 1 Coherence amplitude 1 Phase coherence 0 Trial 2 Coherence amplitude 1 Phase coherence 90 Trial 3 Coherence amplitude 1 Phase coherence 180 COHERENCE = mean(phase vector) Norm 0.33 Phase 90 degree

35 Phase coherence (default) Only phase information component a Only phase information component b

36 Cross-coherence amplitude and phase 5 6 Animal picture Distractor picture Phase (degree) Amplitude (0-1)

37 Two EEG channels C A B Cortex Scalp channel coherence source confounds!

38 MANY EEG channels C A B Cortex Separate out Independent EEG Components Measure their Synchronization source dynamics!

39 Niquist frequency: Aliasing Signal (100 Hz) Sampling (120 Hz) 1 cycle e.g. 100 Hz sampled at 120 Hz

40 Advanced time-frequency functions Tftopo(): allow visualizing time-frequency power distribution over the scalp

41 Plot data spectrum using EEGLAB winsize, 256 (change FFT window length) nfft, 256 (change FFT padding) overlap, 128 (change window overlap)

42 Exercise ALL Start EEGLAB, from the menu load sample_data/eeglab_data_epochs_ica.set or your own data (epoch, reject noise if not done already) Novice From the GUI, Plot spectral decomposition with 100% data and 50% overlap ( overlap ). Try reducing window length ( winsize ) and FFT length ( nfft ) Intermediate Same as novice but using a command line call to the pop_spectopo() function. Use GUI then history to see a standard call ( eegh ). Advanced Same as novice but using a command line call to the spectopo() function. Overlap 50% Padding

43 Exercise - newtimef Novice From the GUI, pick an interesting IC and plot component ERSP. Try changing parameters window size, number of wavelet cycles, padratio, Intermediate From the command line, use newtimef() to tailor your time/ frequency output to your liking. Look up the help to try not to remove the baseline, change baseline length and plot in log scale. Enter custom frequencies and cycles (2 slides back). Advanced Compare FFT, the different wavelet methods (see help), and multi-taper methods (use timef function not newtimef). Enter custom frequencies and cycles. Look up newtimef help to compare conditions. Vizualise single-trial timef-frequency power using erpimage.