Signals and Systems Analysis in Biomedical Enginerring by Northrop, Robert B. -- Read -- Imperial Library of Trantor

Index

Biomedical Engineering Series Dedication Preface Author List of Figures Contents 1Introduction to Biomedical Signals and Systems

1.1General Characteristics of Biomedical Signals

1.1.1Introduction 1.1.2Signals from physiological systems 1.1.3Signals from man-made instruments 1.1.4Discrete signals 1.1.5Some ways to describe signals 1.1.6Introduction to modulation and demodulation of physiological signals

1.2General Properties of Physiological Systems

1.2.1Introduction 1.2.2Analog systems 1.2.3Physiological systems 1.2.4Discrete systems

1.3Summary Problems

2Review of Linear Systems Theory

2.1Linearity, Causality and Stationarity 2.2Analog Systems

2.2.1SISO and MIMO systems 2.2.2Introduction to ODEs and their solutions

2.3Systems Described by Sets of ODEs

2.3.1Introduction 2.3.2Introduction to matrix algebra 2.3.3Some matrix operations 2.3.4Introduction to state variables

2.4Linear System Characterization

2.4.1Introduction 2.4.2System impulse response 2.4.3Real convolution 2.4.4Transient response of systems 2.4.5Steady-state sinusoidal frequency response of LTI systems 2.4.6Bode plots

Example 1:A simple low-pass system Example 2:Underdamped second-order low-pass system described by the ODE: Example 3:A lead/lag filter is described by the ODE:

2.4.7Nyquist plots

2.5Discrete Signals and Systems

2.5.1Introduction 2.5.2Discrete convolution 2.5.3Discrete systems 2.5.4The z transform pair 2.5.5z Transform solutions of discrete state equations 2.5.6Discussion

2.6Stability of Systems 2.7Chapter Summary Problems

3The Laplace Transform and Its Applications

3.1Introduction 3.2Properties of the Laplace Transform 3.3Some Examples of Finding Laplace Transforms 3.4The Inverse Laplace Transform 3.5Applications of the Laplace Transform

3.5.1Introduction 3.5.2Use of partial fraction expansions to find y(t) 3.5.3Application of the Laplace transform to continuous state systems 3.5.4Use of signal flow graphs to find y(t) for continuous state systems 3.5.5Discussion

3.6Chapter Summary Problems

4Fourier Series Analysis of Periodic Signals

4.1Introduction 4.2Properties of the Fourier Series 4.3Fourier Series Examples 4.4Chapter Summary Problems

5The Continuous Fourier Transform

5.1Introduction 5.2Properties of the CFT 5.3Analog-to-Digital Conversion and the Sampling Theorem

5.3.1Introduction 5.3.2Impulse modulation and the Poisson sum form of the sampled spectrum 5.3.3The Sampling Theorem

5.4The Analytical Signal and the Hilbert Transform

5.4.1Introduction 5.4.2The Hilbert transform and the analytical signal 5.4.3Properties of the Hilbert transform 5.4.4An Application of the Hilbert Transform

5.5The Modulation Transfer Function in Imaging

5.5.1Introduction 5.5.2The MTF 5.5.3The contrast transfer function 5.5.4Discussion

5.6Chapter Summary Problems

6The Discrete Fourier Transform

6.1Introduction 6.2The CFT, ICFT, DFT and IDFT

6.2.1The CFT and ICFT 6.2.2Properties of the DFT and IDFT 6.2.3Applications of the DFT and IDFT

6.3Data Window Functions 6.4The FFT

6.4.1Introduction 6.4.2The fast Fourier transform 6.4.3Implementation of the FFT 6.4.4Discussion

6.5Chapter Summary Problems

7Introduction to Time-Frequency Analysis of Biomedical Signals

7.1Introduction 7.2The Short-Term Fourier Transform 7.3Gabor and Adaptive Gabor Transform 7.4Wigner-Ville and Pseudo-Wigner Transforms 7.5Cohen’s General Class of JTF Distributions 7.6Introduction to JTFA Using Wavelets

7.6.1Introduction 7.6.2Computation of the continuous wavelet transform 7.6.3Some wavelet basis functions, (t)

7.7Applications of JTF Analysis to Physiological Signals

7.7.1Introduction 7.7.2Heart sounds 7.7.3JTF analysis of EEG signals 7.7.4Other biomedical applications of JTF spectrograms

7.8JTFA Software 7.9Chapter Summary

8Introduction to the Analysis of Stationary Noise and Signals Contaminated with Noise

8.1Introduction 8.2Noise Descriptors and Noise in Systems

8.2.1Introduction 8.2.2Probability density functions 8.2.3Autocorrelation 8.2.4Cross-Correlation 8.2.5The continuous auto- and cross-power density spectrums 8.2.6Propagation of noise through stationary causal LTI continuous systems 8.2.7Propagation of noise through stationary causal LTI discrete systems 8.2.8Characteristic functions of random variables 8.2.9Price’s theorem and applications 8.2.10Quantization Noise 8.2.11Introduction to “data scrubbing” by nonlinear discrete filtering 8.2.12Discussion

8.3Calculation of Noise Descriptors with Finite Discrete Data 8.4Signal Averaging and Filtering for Signal-to-Noise Ratio Improvement

8.4.1Introduction 8.4.2Analysis of SNR improvement by averaging 8.4.3Introduction to signal-to-noise ratio improvement by linear filtering 8.4.4Discussion

8.5Introduction to the Application of Statistics and Information Theory to Genomics

8.5.1Introduction 8.5.2Review of DNA Biology 8.5.3RNAs and the basics of protein synthesis: transcription and translation 8.5.4Introduction to statistics applied to genomics 8.5.5Introduction to the application of information theory to genomics 8.5.6Introduction to hidden Markov models in genomics 8.5.7Discussion

8.6Chapter Summary Problems

9Basic Mathematical Tools Used in the Characterization of Physiological Systems

9.1Introduction 9.2Some General Properties of Physiological Systems 9.3Some Properties of Nonlinear Systems 9.4Physical Factors Determining the Dynamic Behavior of Physiological Systems

9.4.1Diffusion dynamics 9.4.2Biochemical systems and mass-action kinetics

9.4.2.1Examples of mass action kinetics

9.5Means of Characterizing Physiological Systems

9.5.1Introduction 9.5.2The Nyquist stability criterion 9.5.3Describing functions and the stability of closed-loop nonlinear systems 9.5.4The use of Gaussian noise-based techniques to characterize physiological systems 9.5.5Discussion

9.6Chapter Summary Problems

10The Mathematics of Tomographic Imaging

10.1Introduction 10.2Algebraic Reconstruction 10.3The Radon Transform 10.4The Fourier Slice Theorem 10.5The Filtered Back-Projection Algorithm 10.6Chapter Summary Problems

Appendices Appendix ACramer’s Rule Appendix BSignal Flow Graphs and Mason’s Rule Appendix CBode (Frequency Response) Plots Appendix DComputational Tools for Biomedical Signal Processing and Systems Analysis

D.1Introduction D.2Simnon™ D.3National Instruments’ Lab VIEW™ Signal Processing Tools D.4Matlab, Simulink, and Toolkits D.5Summary

Bibliography and References Index

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