Biomedical Signal Processing

1
Biomedical Signal Processing

• EEG Segmentation
• Joint Time-Frequency Analysis
• Gina Caetano
• 14/10/2004

2
Introduction

• EEG Segmentation
• Spectral error measure
• - Periodogram approach (nonparametric)
• - Whitening approach (parametric)
• 2. Joint Time-Frequency Analysis
• - Linear, nonparametric methods
• - Nonlinear, nonparametric methods
• - Parametric methods

3
EEG Segmentation Spectral Error Measure

• Whitening Approach
• - Parametric
• - AR model (reference window)
• - Linear prediction (test window)
• - Dissimilarity measure ?2(n)

4
EEG segmentation

• AR model of order p describes signal in reference
  window
• Power spectrum of e(n)
• Quadratic spectral error
• measure
• Time domain Asymmetric

5
EEG segmentation

• 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.

6
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 Cohens
  class

• Parametric methods
• - Statistical model with time-varying parameters
• - AR model parameter estimation (slow changes in
  time)

7
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 Cohens
  class

• Parametric methods
• - Statistical model with time-varying parameters
• - AR model parameter estimation (slow changes in
  time)

8
Short-Time Fourier Transform

• 2D modified Fourier transform
• ?(t) length resolution in time and frequency

9
Short-Time Fourier Transform

• Spectrogram

10
Short-Time Fourier Transform

• Spectrogram

EEG
Spectrogram
Diastolic blood pressure
11
Short-Time Fourier Transform

• Spectrogram
• EEG

1 s Hamming window
2 s Hamming window
0.5 s Hamming window
12
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 Cohens
  class

• Parametric methods
• - Statistical model with time-varying parameters
• - AR model parameter estimation (slow changes in
  time)

13
Wigner-Ville Distribution (WVD)

• Ambiguity Function

14
Wigner-Ville Distribution (WVD)

• Ambiguity Function

Analytic signal
Analytic Ambiguity Function
15
Wigner-Ville Distribution (WVD)

• WVD Continuous-time definition

Modulated Gaussian Signal
Spectrogram
WVD
16
Wigner-Ville Distribution (WVD)

• WVD Limitations

Two-components Signal
Spectrogram
Wigner-Ville distribution
17
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 Cohens
  class

• Parametric methods
• - Statistical model with time-varying parameters
• - AR model parameter estimation (slow changes in
  time)

18
Cohens class

• General time-frequency distribution

Wigner-Ville distribution
pseudoWigner-Ville distribution
Spectrogram
Choi-Williams distribution
19
Cohens class

• Choi-Williams distribution

Two-components Signal
Wigner-Ville distribution
Choi-William distribution
20
Cohens class

• Choi-Williams distribution

EEG
Spectrogram
Wigner-Ville distribution
Choi-William distribution
21
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 Cohens
  class

• Parametric methods
• - Statistical model with time-varying parameters
• - AR model parameter estimation (slow changes in
  time)

22
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

23
Model-based analysis of slowly varying signals

• LSM Algorithm (AR model, p8)