Biomedical Signal Processing and Signal Modeling
	Eugene N. Bruce, Center for Biomedical Engineering, University of Kentucky

The following supplementary materials are available by request as compressed (ZIP) files (send an email to ebruce@uky.edu):

Data files used for examples and problems in the book.   M-files used for examples in the book.   Simulink model files referenced in the book.

Table of Contents

Chapter 1: The nature of biomedical signals

• 1.1 The reasons for studying biomedical signal processing
• 1.2 What is a signal?
• 1.3 Some typical sources of biomedical signals
• 1.4 Continuous-time and discrete-time
• 1.5 Assessing the relationships between two signals
• 1.6 Why do we "process" signals?
• 1.7 Types of signals: deterministic, stochastic, fractal and chaotic
• 1.8 Signal modeling as a framework for signal processing
• 1.9 What is noise?
• 1.10 Summary
• Exercises

  Chapter 2: Memory and correlation

• 2.1 Introduction
• 2.2 Properties of operators and transformations
• 2.3 Memory in a physical system
• 2.4 Energy and power signals
• 2.5 The concept of autocorrelation
• 2.6 Autocovariance and autocorrelation for DT signals
• 2.7 Summary
• Exercises

  Chapter 3: The impulse response

• 3.1 Introduction
• 3.2 Thought experiment and computer exercise: glucose control
• 3.3 Convolution form of an LSI system
• 3.4 Convolution for continuous-time systems
• 3.5 Convolution as signal processing
• 3.6 Relation of impulse response to differential equation
• 3.7 Convolution as a filtering process
• 3.8 Impulse responses for nonlinear systems
• 3.9 The glucose control problem, revisited
• 3.10 Summary
• Exercises

  Chapter 4: Frequency Response

• 4.1 Introduction
• 4.2 Biomedical example (Transducers for measuring knee angle)
• 4.3 Sinusoidal inputs to LTIC systems
• 4.4 Generalized frequency response
• 4.5 Frequency response of discrete-time systems
• 4.6 Series and parallel filter cascades
• 4.7 Ideal filters
• 4.8 Frequency response and nonlinear systems
• 4.9 Other biomedical examples
• 4.10 Summary
• Exercises

  Chapter 5: Modeling continuous-time signals as sums of sine waves

• 5.1 Introduction
• 5.2 Introductory example (Analysis of circadian rhythm)
• 5.3 Orthogonal functions
• 5.4 Sinusoidal basis functions
• 5.5 The Fourier series
• 5.6 The frequency response and nonsinusoidal periodic inputs
• 5.7 Parseval's relation for periodic signals
• 5.8 The Continuous-Time Fourier Transform (CTFT)
• 5.9 Relationship of Fourier Transform to frequency response
• 5.10 Properties of the Fourier Transform
• 5.11 The generalized Fourier Transform
• 5.12 Examples of Fourier Transform calculations
• 5.13 Parseval's relation for nonperiodic signals
• 5.14 Filtering
• 5.15 Output response via the Fourier Transform
• 5.16 Summary
• Exercises

  Chapter 6: Responses of linear continuous-time filters to arbitrary inputs

• 6.1 Introduction
• 6.2 Introductory example
• 6.3 Conceptual basis of the LaPlace Transform
• 6.4 Properties of (unilateral) LaPlace Transforms
• 6.5 The inverse (unilateral) LaPlace Transform
• 6.6 Transfer functions
• 6.7 Feedback systems
• 6.8 Biomedical applications of LaPlace Transforms
• 6.9 Summary
• Exercises

  Chapter 7: Modeling signals as sums of discrete-time sine waves

• 7.1 Introduction
• 7.2 Interactive example: Periodic oscillations in the amplitude of breathing
• 7.3 The discrete-time Fourier series
• 7.4 Fourier Transform of discrete-time signals
• 7.5 Parseval's Relation for DT nonperiodic signals
• 7.6 Output of an LSI system
• 7.7 Relation of DFS and DTFT
• 7.8 Windowing
• 7.9 Sampling
• 7.10 The Discrete Fourier Transform (DFT)
• 7.11 Biomedical applications
• 7.12 Summary
• Exercises

  Chapter 8: Noise Removal and Signal Compensation

• 8.1 Introduction
• 8.2 Introductory example: Reducing the ECG artifact in an EMG recording
• 8.3 Eigenfunctions of LSI systems and the Z-transform
• 8.4 Properties of the bilateral Z-transform
• 8.5 Poles and zeros of Z-transforms
• 8.6 The inverse Z-transform
• 8.7 Pole locations and time responses
• 8.8 The unilateral Z-transform
• 8.9 Analyzing digital filters using Z-transforms (DT Transfer functions)
• 8.10 Biomedical applications of DT filters
• 8.11 Overview: Design of digital filters
• 8.12 IIR filter design by approximating a CT filter
• 8.13 IIR filter design by impulse invariance
• 8.14 IIR filter design by bilinear transformation
• 8.15 Biomedical examples of IIR digital filter design
• 8.16 IIR filter design by minimization of an error function
• 8.17 FIR filter design
• 8.18 Frequency-band transformations
• 8.19 Biomedical applications of digital filtering
• 8.20 Summary
• Exercises

  Chapter 9: Modeling stochastic signals as filtered white noise

• 9.1 Introduction
• 9.2 Introductory exercise: EEG analysis
• 9.3 Random processes
• 9.4 Mean and autocorrelation function of a random process
• 9.5 Stationarity and ergodicity
• 9.6 General linear processes
• 9.7 Yule-Walker equations
• 9.8 Autoregressive (AR) processes
• 9.9 Moving average (MA) processes
• 9.10 Autoregressive-Moving Average (ARMA) processes
• 9.11 Harmonic processes
• 9.12 Other biomedical examples
• 9.13 Introductory example, cont.
• 9.14 Summary
• Exercises

  Chapter 10: Scaling and long-term memory

• 10.1 Introduction
• 10.2 Geometrical scaling and self-similarity
• 10.3 Measures of dimension
• 10.4 Self-similarity and functions of time
• 10.5 Theoretical signals having statistical similarity
• 10.6 Measures of statistical similarity for real signals
• 10.7 Generation of synthetic fractal signals
• 10.8 Fractional differencing models
• 10.9 Biomedical examples
• 10.10 Summary

  Exercises

  Chapter 11: Nonlinear models of signals

• 11.1 Introductory exercise
• 11.2 Nonlinear signals and systems: basic concepts
• 11.3 Poincare' sections and return maps
• 11.4 Chaos
• 11.5 Measures of nonlinear signals and systems
• 11.6 Characteristic multipliers and Lyapunov exponents
• 11.7 Estimating the dimension of real data
• 11.8 Tests of null hypotheses based on surrogate data
• 11.9 Other biomedical applications
• 11.10 Summary
• Exercises

  Chapter 12: Assessing stationarity and reproducibility

• 12.1 Introduction
• 12.2 Assessing stationarity of a random process from a sample function
• 12.3 Statistical properties of autocovariance estimators
• 12.4 Statistical properties of the periodogram
• 12.5 Analysis of nonstationary signals
• 12.6 Nonstationary second-order statistics
• 12.7 Summary
• Exercises

  A1. Appendix 1: References