Biomedical Signal Processing
EEG Segmentation
&
Joint Time-Frequency Analysis
Gina Caetano
14/10/2004
Introduction
1. EEG SegmentationSpectral error measure:- Periodogram approach (nonparametric) - Whitening approach (parametric)
2. Joint Time-Frequency Analysis- Linear, nonparametric methods- Nonlinear, nonparametric methods- Parametric methods
EEG Segmentation: Spectral Error Measure
Whitening Approach
- Parametric
- AR model (reference window)
- Linear prediction (test window)
- Dissimilarity measure Δ2(n)
• AR model of order p describes signal in reference window
Power spectrum of e(n)
Quadratic spectral error
measure
Time domain Asymmetric
k
kje
je enkrneS ,,
EEG segmentation
20,00, eej
e reS
2
22
2
,21
,21
dneS
dneSn
je
ej
e
M
ke
ee
e nkrnrnr
rn
1
22
2
2 ,,0
21
,0
0,0
• AR model of order p describes signal in reference window
Simpler Asymmetric
ad hoc “reverse” test
Symmetric
Simulations: prediction-based method associated with lower false alarm rate than correlation-method.
EEG segmentation
1
0
2
3 10,0
11
0,0
,0 tN
k ete
e
r
kne
Nr
nrn
r
t
t
r
N
k e
r
r
N
k e
t
t nr
ke
Nr
kne
Nn
1
2
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2
4 1,0
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1
Joint Time-Frequency Analysis
• When in time different frequencies of signal are present
Linear, nonparametric methods
- Linear filtering operation
- Short-time Fourier transform
- Wavelet transform
Nonlinear, nonparametric methods
- Wigner-Ville Distribution (ambiguity function)
- General Time-Frequency distributions – Cohen’s class
Parametric methods
- Statistical model with time-varying parameters
- AR model parameter estimation (slow changes in time)
Joint Time-Frequency Analysis
• When in time different frequencies of signal are present
Linear, nonparametric methods
- Linear filtering operation
- Short-time Fourier transform
- Wavelet transform
Nonlinear, nonparametric methods
- Wigner-Ville Distribution (ambiguity function)
- General Time-Frequency distributions – Cohen’s class
Parametric methods
- Statistical model with time-varying parameters
- AR model parameter estimation (slow changes in time)
Short-Time Fourier Transform
2D modified Fourier transform
ω(t) length resolution in time and frequency
detxtX j,
0.lim
txtt
Spectrogram
Uncertainty Principle Only Fourier-based spectral analysis
2,, tXtSx
2/1 t
Short-Time Fourier Transform
Spectrogram
Short-Time Fourier Transform
Spectrogram
EEG
Spectrogram
Diastolic blood pressure
Short-Time Fourier Transform
SpectrogramEEG
1 s Hamming window
2 s Hamming window
0.5 s Hamming window
Joint Time-Frequency Analysis
Linear, nonparametric methods
- Linear filtering operation
- Short-time Fourier transform
- Wavelet transform
Nonlinear, nonparametric methods
- Wigner-Ville Distribution (ambiguity function)
- General Time-Frequency distributions – Cohen’s class
Parametric methods
- Statistical model with time-varying parameters
- AR model parameter estimation (slow changes in time)
Wigner-Ville Distribution (WVD)
• Ambiguity Function
dtetxtxA tj
x 2/2/*,
deAS jxx 0,Energy Density Spectrum
dttxAx
20,0Energy Function Maximum
Wigner-Ville Distribution (WVD)
• Ambiguity Function
1,, jsx eAA
A
tjA etstx 1
Analytic signal
Analytic Ambiguity Function
Wigner-Ville Distribution (WVD)
• WVD: Continuous-time definition
detxtxddeeAtW jjtjxx
22
*,2
1,
Modulated Gaussian Signal
Spectrogram
WVD
Wigner-Ville Distribution (WVD)
• WVD: Limitations
Two-components Signal
Spectrogram
Wigner-Ville distribution
Joint Time-Frequency Analysis
Linear, nonparametric methods
- Linear filtering operation
- Short-time Fourier transform
- Wavelet transform
Nonlinear, nonparametric methods
- Wigner-Ville Distribution (ambiguity function)
- General Time-Frequency distributions – Cohen’s class
Parametric methods
- Statistical model with time-varying parameters
- AR model parameter estimation (slow changes in time)
Cohen’s class
• General time-frequency distribution
ddeeAgtC jtjxx ,,
2
1,
1, gWigner-Ville distribution
pseudoWigner-Ville distribution ,g
Spectrogram dtettg tj
22,
Choi-Williams distribution )4/(22
, eg
Cohen’s class
• Choi-Williams distribution
Two-components Signal
Wigner-Ville distribution
Choi-William distribution
Cohen’s class• Choi-Williams distribution
Spectrogram
Choi-William distribution
EEG
Wigner-Ville distribution
Joint Time-Frequency Analysis
Linear, nonparametric methods
- Linear filtering operation
- Short-time Fourier transform
- Wavelet transform
Nonlinear, nonparametric methods
- Wigner-Ville Distribution (ambiguity function)
- General Time-Frequency distributions – Cohen’s class
Parametric methods
- Statistical model with time-varying parameters
- AR model parameter estimation (slow changes in time)
Model-based analysis of slowly varying signals
Parametric model of signal Time-varying AR model Slow temporal variations Time-varying noise
Two adaptive methods Minimization of prediction error LMS: minimizes forward prediction error variance Gradient Adaptive Lattice: minimizes forward and
backward prediction error variances
Model-based analysis of slowly varying signals
LSM Algorithm (AR model, p=8)