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

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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

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EEG Segmentation: Spectral Error Measure Whitening Approach - Parametric - AR model (reference window) - Linear prediction (test window) - Dissimilarity measure Δ 2 (n)

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

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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

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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)

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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)

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

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Short-Time Fourier Transform Spectrogram

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Short-Time Fourier Transform Spectrogram EEG Spectrogram Diastolic blood pressure

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Short-Time Fourier Transform Spectrogram EEG 1 s Hamming window 2 s Hamming window 0.5 s Hamming window

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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)

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

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

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

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

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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)

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Cohens class General time-frequency distribution Wigner-Ville distribution pseudoWigner-Ville distribution Spectrogram Choi-Williams distribution

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

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

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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)

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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

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Model-based analysis of slowly varying signals LSM Algorithm (AR model, p=8)

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