EEGLAB2010 AD Nov18 Time Frequency Dec Om Positions
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Transcript of 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