Biomedical Signal Processing EEG Segmentation & Joint Time-Frequency Analysis Gina Caetano 14/10/2004.

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

1

2

4 1,0

11

0,0

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)