Bài giảng Biomedical signal processing and modeling - Frequency Domain Characterization

Nội dung text: Bài giảng Biomedical signal processing and modeling - Frequency Domain Characterization

1. Nguyễn Công Phương BIOMEDICAL SIGNAL PROCESSING AND MODELING Frequency Domain Characterization
2. Contents I. Introduction II. Concurrent, Coupled, and Correlated Processes III. Filtering for Removal of Artifacts IV. Detection of Events V. Analysis of Waveshape and Waveform Complexity VI. Frequency Domain Characterization VII.Modeling Biomedical Systems VIII.Analysis of Nonstationary and Multicomponent Signals IX. Pattern Classification and Diagnostic Decision sites.google.com/site/ncpdhbkhn 2
3. Frequency Domain Characterization 1. Introduction 2. Estimation of the PSD 3. Measures Derived from PSDs sites.google.com/site/ncpdhbkhn 3
4. Introduction • Many biomedical exhibit innate rhythms and periodicity that are more readily expressed & appreciated in terms of frequency than temporal measures. • Problems: – Investigate the potential use of the Fourier spectrum & parameters derived thereof in the analysis of biomedical signals. – Identify physiological & pathological processes that could modify the frequency content of the corresponding signals. Example of the time signal and corresponding power spectral density.... | Download Scientific Diagram (researchgate.net) sites.google.com/site/ncpdhbkhn 4
5. Frequency Domain Characterization 1. Introduction 2. Estimation of the PSD 3. Measures Derived from PSDs sites.google.com/site/ncpdhbkhn 5
6. Estimation of the PSD − − 1 N m 1 φ []m= x [][ n x n + m ] 1 −  N m n=0 N− m − 1 φ =1 + 2[]m x [][ n x n m ] N n=0 N− m φ[]m= φ [] m 2N 1 sites.google.com/site/ncpdhbkhn 6
7. Frequency Domain Characterization 1. Introduction 2. Estimation of the PSD a) The periodogram b) The need for averaging c) The modified periodogram d) The Blackman – Tukey method: Smoothing a single periodogram e) The Bartlett – Welch method: Averaging multiple periodograms 3. Measures Derived from PSDs sites.google.com/site/ncpdhbkhn 7
8. The periodogram (1) n−1 ω= φ − jω m S2() 2 [] m e 2 m=−( N − 1 ) X (ω ) →ω = S2( ) N −1 N X()ω =  xne [] − jω n n=0 N −1 N− m ω= φ − jω m ES[2 ( )] xx [ me ] m=−( N − 1 ) N n−1 ω= φ − jω m S1() 1 [] m e m=−( N − 1 ) N −1 ω= φ − jω m ES[()]1  xx [] me m=−( N − 1 ) sites.google.com/site/ncpdhbkhn 8
9. The periodogram (2) Signal Periodogram sites.google.com/site/ncpdhbkhn 9
10. Frequency Domain Characterization 1. Introduction 2. Estimation of the PSD a) The periodogram b) The need for averaging c) The modified periodogram d) The Blackman – Tukey method: Smoothing a single periodogram e) The Bartlett – Welch method: Averaging multiple periodograms 3. Measures Derived from PSDs sites.google.com/site/ncpdhbkhn 10