Bài giảng Biomedical signal processing and modeling - Filtering for Removal of Artifact

Nội dung text: Bài giảng Biomedical signal processing and modeling - Filtering for Removal of Artifact

1. Nguyễn Công Phương BIOMEDICAL SIGNAL PROCESSING AND MODELING Filtering for Removal of Artifact
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. Filtering for Removal of Artifacts 1. Introduction 2. Random, Structured, and Physiological Noise 3. Illustration of the Problem with Case Studies 4. Fundamental Concepts of Filtering 5. Time-domain Filters 6. Frequency-domain Filters 7. Optimal Filtering: the Wiener Filter 8. Adaptive Filters for Removal of Interference 9. Selecting an Appropriate Filter sites.google.com/site/ncpdhbkhn 3
4. Introduction • Noise is everywhere: – During a procedure to acquire the ECG signal, if the subject coughs or squirms, the EMG associated with such activity will create an interference or artifact. – Electronic noise in the instrumentation amplifiers also gets amplified along with the desired signal. – Our environment is filled with EM waves, both natural and man-made. – • This chapter is to analyze the various types of artifacts that corrupt biomedical signals and explore filtering techniques to remove them without degrading the signal of interest. sites.google.com/site/ncpdhbkhn 4
5. Filtering for Removal of Artifacts 1. Introduction 2. Random, Structured, and Physiological Noise 1. Random noise 2. Structured noise 3. Physiological interference 4. Stationary, nonstationary, and cyclostationary processes 3. Illustration of the Problem with Case Studies 4. Fundamental Concepts of Filtering 5. Time-domain Filters 6. Frequency-domain Filters 7. Optimal Filtering: the Wiener Filter 8. Adaptive Filters for Removal of Interference 9. Selecting an Appropriate Filter sites.google.com/site/ncpdhbkhn 5
6. Random noise (1) • A deterministic signal is one whose value at a given instant of time may be computed using a closed-form mathematical function of time, or predicted from a knowledge of a few past values of the signal. • A signal that does not meet this condition may be labeled as a nondeterministic signal or a random signal. • Given a signal of N samples, the signal may be labeled as being random if the number of turning points is greater than the threshold 2( N – 2)/3. sites.google.com/site/ncpdhbkhn 6
7. Random noise (2) ∞ Mean value/ Expectation :m= E( X ) = xf ( x ) dx x −∞ X ∞ 2 2 2 ση=var( η ) = E[( η −m η ) ] = ( η − mfd ηη ) ( η ) η −∞ 2 2 =E(η ) − mη Standard deviation :ση = var( η ) sites.google.com/site/ncpdhbkhn 7
8. Random noise (3) ση Coefficient variation : CV = mη ∞ 1 3 Skewness :Sη= (η − mfd η ) η ( η ) η 3 −∞ ση 1 ∞ Kurtosis :K= (η − mfd )4 ( η ) η η4 −∞ η η ση ∞ Entropy :Hη= − f η (η )log fd η ( η ) η −∞ 2 sites.google.com/site/ncpdhbkhn 8
9. Random noise (4) N = 1 η Mean value : mη  i N i=1 N = 1 η 2 Mean square : MS η  i N i=1 N = 1 η 2 Root mean square : RMS η  i N i=1 N σ=1 η − 2 Standard deviation :η (i m η ) N i=1 N = − η η Entropy :Hη p η (l )log2 [ p η ( l )] l=1 sites.google.com/site/ncpdhbkhn 9
10. Random noise (5) yt()= xt () +η () t η= η Ifpx,η (,) x pxp x () η () thenx andη arestatisticallyindependent = = + E(y ) my m x mη −2 =σ 2 = σ 2 + σ 2 E[(y my ) ] y x η sites.google.com/site/ncpdhbkhn 10