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Biomedical Signal Processing

Biomedical Signal Processing. EEG Segmentation & Joint Time-Frequency Analysis Gina Caetano 14/10/2004. Introduction. EEG Segmentation Spectral error measure: - Periodogram approach (nonparametric) - Whitening approach (parametric) 2. Joint Time-Frequency Analysis

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Biomedical Signal Processing

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  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 Δ2(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 • Linear, nonparametric methods - Linear filtering operation - Short-time Fourier transform - Wavelet transform • When in time different frequencies of signal are present • 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)

  7. Joint Time-Frequency Analysis • Linear, nonparametric methods - Linear filtering operation -Short-time Fourier transform - Wavelet transform • When in time different frequencies of signal are present • 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)

  8. Spectrogram Uncertainty Principle Only Fourier-based spectral analysis Short-Time Fourier Transform 2D modified Fourier transform ω(t) length resolution in time and frequency

  9. Short-Time Fourier Transform • Spectrogram

  10. Short-Time Fourier Transform EEG • Spectrogram 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 – Cohen’s class • Parametric methods - Statistical model with time-varying parameters - AR model parameter estimation (slow changes in time)

  13. Energy Density Spectrum Energy Function Maximum 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) Two-components Signal • WVD: Limitations 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 – Cohen’s class • Parametric methods - Statistical model with time-varying parameters - AR model parameter estimation (slow changes in time)

  18. Cohen’s class • General time-frequency distribution Wigner-Ville distribution pseudoWigner-Ville distribution Spectrogram Choi-Williams distribution

  19. Cohen’s class • Choi-Williams distribution Two-components Signal Wigner-Ville distribution Choi-William distribution

  20. Cohen’s 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 – Cohen’s 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, p=8)

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