EEGLAB2010 AD Nov18 Time Frequency Dec Om Positions

8/3/2019 EEGLAB2010 AD Nov18 Time Frequency Dec Om Positions

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Time-Frequency analysis of

biophysical time series

Arnaud Delorme

SCCN, UCSD

CERCO, CNRS

Nov 18th 2010, 12th EEGLAB workshop


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Frequency analysis

1 second

4-7 Hz Theta

9-11 Hz Alpha

18-21 Hz Beta

30-60 Hz Gamma

0.5-2 Hz Delta

synchronicity of cellexcitation determines

amplitude and rhythmof the EEG signal


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Frequency analysis

Delta

Theta

Alpha

Beta

Low Delta


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Stationary signals

TimeTime

Time Time

Magn

itude

Magnitude

Mag

nitude

Magnitude

Slide courtesy of Petros Xanthopoulos, Univ. of Florida

10 Hz2 Hz

2+10+20 Hz20 Hz


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Stationary signal

Time

Magnitude

Magnitude

Frequency (Hz)

2 Hz + 10 Hz + 20Hz

Stationary

By looking at the Power spectrum of the signal we can recognize three frequency

Components (at 2,10,20Hz respectively).

Power spectrum

Slide courtesy of Petros Xanthopoulos, Univ. of Florida


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Figure, courtesy of Ravi Ramamoorthi & Wolberg

Freq. decomp. Sum of freq.Time

domain

Time

Frequency

Forward

transform

Inverse

transform

Frequency

domain

du


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*

Time

EEGa

mplitud

e

Sinusoid

Gaussian

Tapered

sinusoid

Performing Fourier

transform by using

a time movingwindow


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Spectral phase and amplitude

Real

Imaginary

Real

Imag.

Fk(f,t)


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Real

Imag.

Real

Imaginary

Spectral phase and amplitude

Fk(f,t)


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Discrete Fourrier Transform function

function X = dft(x)

[N,M] = size(x);

n = 0:N-1;

for k=n

X(k+1) = exp(-j*2*pi*k*n/N)*x;end

Loop on frequency

Real part

Cosine component

Imaginary part

Sine component

Multiply with signal


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Average of squared absolute values


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Spectral power

0 Hz 10 Hz 20 Hz 30 Hz 40 Hz 50 Hz

Powe

r(dB)

Frequency (Hz)

Average of squared amplitude


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Average of squared amplitudes

Overlap 50%


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padding


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Spectrogram or ERSP

0 ms 10 ms 20 ms 30 ms 40 ms 50 ms 60 ms

5 Hz

10 Hz

20 Hz

30 Hz


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Spectrogram or ERSP

0 ms 10 ms 20 ms 30 ms 40 ms 50 ms 60 ms

5 Hz

10 Hz

20 Hz

30 Hz

5 Hz

10 Hz

20 Hz

30 Hz

0 ms 10 ms 20 ms 30 ms 40 ms 50 ms 60 ms

Average of

squaredvalues


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Complex number

Scaled to dB 10Log10(ERSP)

Power spectrum and

event-related spectral perturbation


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Absolute versus relative power

Absolute = ERS

Relative = ERSP (dB or %)


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Difference between FFT and wavelets

FFT Wavelet

Frequency


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Wavelets factor

Wavelet (0)= FFT Wavelet (1)

1Hz

2Hz

4Hz

6Hz

8Hz

10Hz


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Time-frequency resolution trade off


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FFT

In between

Pure wavelet


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The Uncertainty Principle

A signal cannot be localizedarbitrarily well both in time/position and in frequency/

momentum.There exists a lower bound tothe Heisenbergs product:

tf 1/(4)

f = 1Hz, t = 80 msec orf = 2Hz, t = 40 msec


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Modified wavelets

Wavelet (0.8) Wavelet (0.5) Wavelet (0.2)


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Inter trial coherence

amplitude 0.5 phase 0

amplitude 1 phase 90

amplitude 0.25 phase 180

COHERENCE = mean(phase vector)

Norm 0.33

POWER = mean(amplitudes2 )

0.44 or 8.3 dB

same time, different trials

Trial1

Tr

ial2

Trial3


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Slide courtesy of Stefan Debener


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Normalized

(no amplitude information)

Phase ITC


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Power and inter trial coherence

Attend left-stim left Attend left-stim right

dB

ITC: trials synchronization

5

Difference


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Plot IC ERSP


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Mask IC ERSP

0.01

Pure green denotes

non-significant points


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Plot IC ERSP

Increase# freq bins

padratio = 1 padratio = 2


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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

1 2 3 4 5 6

1 2 3 4 5 6


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Component time-frequency


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Cross-coherence amplitude and phase

2 components, comparison on the same trials

Coherence amplitude 1

Phase coherence 0

Coherence amplitude 1

Phase coherence 90

Coherence amplitude 1Phase coherence 180

Trial1

Trial2

Trial3

COHERENCE = mean(phase vector)Norm 0.33

Phase 90 degree


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Only phase information component a

Only phase information component b

Phase coherence (default)


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Cross-coherence amplitude

and phase

Animal picture Distractor picture

Phase(

degree)

Amplitude(0-1)

5 6


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Cortex

Two EEG channels

A

Scalp channel coherence source confounds!

BC


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Cortex

CA B

MANY EEG channels

source dynamics!

Independent EEG

Components

Separate out

SynchronizationMeasure their


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Niquist frequency: Aliasing

1 cycle

e.g. 100 Hz sampled at 120 Hz

Signal (100 Hz) Sampling (120 Hz)


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Advanced

time-frequency functions Tftopo(): allow visualizing time-frequency

power distribution over the scalp


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Plot data spectrum using EEGLAB

winsize, 256 (change FFT window length)

nfft, 256 (change FFT padding)overlap, 128 (change window overlap)


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Exercise

ALLStart EEGLAB, from the menu loadsample_data/eeglab_data_epochs_ica.set

or your own data (epoch, reject noise if notdone already)

NoviceFrom the GUI, Plot spectral decompositionwith 100% data and 50% overlap (overlap).Try reducing window length (winsize) andFFT length (nfft)

IntermediateSame as novice but using a command line

call to thepop_spectopo() function. Use GUIthen history to see a standard call (eegh).

AdvancedSame as novice but using a command linecall to the spectopo() function.

Overlap 50%

Padding

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EEGLAB2010 AD Nov18 Time Frequency Dec Om Positions