Bài giảng Biomedical signal processing and modeling - Modeling Biomedical Systems

Nội dung text: Bài giảng Biomedical signal processing and modeling - Modeling Biomedical Systems

1. Nguyễn Công Phương BIOMEDICAL SIGNAL PROCESSING AND MODELING Modeling Biomedical Systems
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. Modeling Biomedical Systems 1. Introduction 2. Point Processes 3. Parametric System Modeling 4. Autoregressive or All-pole Modeling 5. Pole-zero Modeling 6. Electromechanical Models of Signal Generation sites.google.com/site/ncpdhbkhn 3
4. Introduction • Propose mathematical models to represent the generation of biomedical signals. • Identify the possible relationships between the mathematical models & the physiological & pathological processes & systems that generate the signals. • Explore the potential use of the model parameters in signal analysis, pattern recognition, & classification. sites.google.com/site/ncpdhbkhn 4
5. Modeling Biomedical Systems 1. Introduction 2. Point Processes 3. Parametric System Modeling 4. Autoregressive or All-pole Modeling 5. Pole-zero Modeling 6. Electromechanical Models of Signal Generation sites.google.com/site/ncpdhbkhn 5
6. Point Processes (1) N =δ − xt() ( tt i ) i=0 ∞ N N − ω − jω t X()ω= δ () ttedt −j t = e i −∞ i  i=0 i = 0 N − ω X()ω= EX [()] ω =  Ee [j t i ] i=0 ∞ −jtω − jt ω Ee[]i= e i ptdt () −∞ ti i i 1 (t− i µ ) 2 = − i pt( t i ) exp i σ2 π i 2iσ 2 ∞ 2 − ω 1 (t− i µ ) →=E ej t i − jω t − i dt [ ] exp(i )exp 2 i σ2 π i −∞ 2iσ sites.google.com/site/ncpdhbkhn 6
7. Point Processes (2) ∞ − µ 2 − jω t 1 (t i ) i = −ω − i Ee[ ] exp( jti )exp 2 dt i σ2 π i −∞ 2iσ = − µ r ti i − ω µ j i ∞ 2 − jω t e r →=i −ω − E[ e ] exp( j r )exp 2 dr σ2 π i −∞ 2iσ 2 σ2 ω 2 − t − e2σ 2 →Fourier transform σ2 π e 2 2 2 − ω iσ ω →Ee[j t i ] =− exp( jiω µ ) exp − 2 N − jω t X()ω =  E [ e i ] i=0 N iσ2 ω 2 →=X(ω ) exp( − j ω i µ )exp − i=0 2 sites.google.com/site/ncpdhbkhn 7
8. Modeling Biomedical Systems 1. Introduction 2. Point Processes 3. Parametric System Modeling 4. Autoregressive or All-pole Modeling 5. Pole-zero Modeling 6. Electromechanical Models of Signal Generation sites.google.com/site/ncpdhbkhn 8
9. Parametric System Modeling (1) P Q =− −+ − yn[] aynkk [] G  bxnl l [] k=1 l = 0 • bl, l = 0, 1, 2, . . . , Q, indicate how the present and Q past samples of the input are combined, in a linear manner, to generate the present output sample. • ak, k = 1, 2, . . . , P, indicate how the past P samples of the output are linearly combined (in a feedback loop) to produce the current output. • G is a gain factor. • P and Q determine the order of the system. sites.google.com/site/ncpdhbkhn 9
10. Parametric System Modeling (2) P Q =− −+ − yn[] aynkk [] G  bxnl l [] k=1 l = 0 • The summation over x represents the moving-average or MA part of the system. • The summation over y represents the autoregressive or AR part of the system. • The entire system may be viewed as a combined autoregressive, moving-average or ARMA system. • The output of the system is simply a linear combination of the present input sample, a few past input samples, and a few past output samples. • The use of the past input and output samples in computing the present output sample represents the memory of the system. The model also indicates that the present output sample may be predicted as a linear combination of the present and a few past input samples, and a few past output samples linear prediction (LP) model. sites.google.com/site/ncpdhbkhn 10