Biomedical Signal Processing EEG Segmentation Joint TimeFrequency Analysis

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

Introduction 1. EEG Segmentation Spectral 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 Δ 2(n)

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

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.

Joint Time-Frequency Analysis • When in time different frequencies of signal are present q Linear, nonparametric methods - Linear filtering operation - Short-time Fourier transform - Wavelet transform q Nonlinear, nonparametric methods - Wigner-Ville Distribution (ambiguity function) - General Time-Frequency distributions – Cohen’s class q Parametric methods - Statistical model with time-varying parameters - AR model parameter estimation (slow changes in time)

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

Short-Time Fourier Transform q Spectrogram

Short-Time Fourier Transform q Spectrogram EEG Spectrogram Diastolic blood pressure

Short-Time Fourier Transform q Spectrogram EEG 1 s Hamming window 2 s Hamming window 0. 5 s Hamming window

Joint Time-Frequency Analysis q Linear, nonparametric methods - Linear filtering operation - Short-time Fourier transform - Wavelet transform q Nonlinear, nonparametric methods - Wigner-Ville Distribution (ambiguity function) - General Time-Frequency distributions – Cohen’s class q Parametric methods - Statistical model with time-varying parameters - AR model parameter estimation (slow changes in time)

Wigner-Ville Distribution (WVD) • Ambiguity Function Energy Density Spectrum Energy Function Maximum

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

Wigner-Ville Distribution (WVD) • WVD: Continuous-time definition Modulated Gaussian Signal Spectrogram WVD

Wigner-Ville Distribution (WVD) • WVD: Limitations Two-components Signal Spectrogram Wigner-Ville distribution

Joint Time-Frequency Analysis q Linear, nonparametric methods - Linear filtering operation - Short-time Fourier transform - Wavelet transform q Nonlinear, nonparametric methods - Wigner-Ville Distribution (ambiguity function) - General Time-Frequency distributions – Cohen’s class q Parametric methods - Statistical model with time-varying parameters - AR model parameter estimation (slow changes in time)

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

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

Cohen’s class • Choi-Williams distribution EEG Spectrogram Wigner-Ville distribution Choi-William distribution

Joint Time-Frequency Analysis q Linear, nonparametric methods - Linear filtering operation - Short-time Fourier transform - Wavelet transform q Nonlinear, nonparametric methods - Wigner-Ville Distribution (ambiguity function) - General Time-Frequency distributions – Cohen’s class q Parametric methods - Statistical model with time-varying parameters - AR model parameter estimation (slow changes in time)

Model-based analysis of slowly varying signals q q Parametric model of signal Time-varying AR model Slow temporal variations Time-varying noise q q 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 q LSM Algorithm (AR model, p=8)