#### Get Citation

The interdisciplinary field of biomedical engineering requires its practitioners to master not only engineering skills, but also a diversity of material in the biological sciences. This text helps biomedical engineers strengthen their skills in the common network of applied mathematics that ties together these diverse disciplines. Based on the author's 30 years of experience in teaching as well as his personal research on neurosensory systems, Signals and Systems Analysis in Biomedical Engineering provides a ready source of information on those specialized mathematical techniques most useful in describing and analyzing biomedical signals, including ECG, EEG, blood pressure, biochemical spectrograms, and tomographic images.

Enriched with many examples that promote sound practical analysis, this book:

INTRODUCTION TO BIOMEDICAL SIGNALS AND SYSTEMS

General Characteristics of Biomedical Signals

General Properties of Physiological Systems

Chapter Summary

REVIEW OF LINEAR SYSTEMS THEORY

Linearity; Causality, Stationarity

Analog Systems

Systems Described by Sets of ODEs

Linear System Characterization

Discrete Systems and Signals

Stability of Systems

Chapter Summary

THE LAPLACE TRANSFORM AND ITS APPLICATIONS

Introduction

Properties of the Laplace Transform

Some Examples of Finding Laplace Transforms

The Inverse Laplace Transform

Applications of the Laplace Transform

Chapter Summary

FOURIER SERIES ANALYSIS OF PERIODIC SIGNALS

Introduction

Properties of the Fourier Series

Fourier Series Examples

Chapter Summary

THE CONTINUOUS FOURIER TRANSFORM

Introduction

Properties of the CFT

Analog-to-Digital Conversion and the Sampling Theorem

The Analytical Signal and the Hilbert Transform

The Modulation Transfer Function in Imaging

Chapter Summary

THE DISCRETE FOURIER TRANSFORM

Introduction

The CFT, ICFT, DFT and IDFT

Data Window Functions

The FFT

Chapter Summary

INTRODUCTION TO TIME-FREQUENCY ANALYSIS OF BIOMEDICAL SIGNALS

Introduction

The Short-term Fourier Transform (STFT)

Gabor and Adaptive Gabor Transform

Wigner-Ville & Pseudo-Wigner Transforms

Cohen's General Class of JTF Distributions

Introduction to JTFA Using Wavelets

Applications of JTF Analysis to Physiological Signals

JTFA Software

Chapter Summary

INTRODUCTION TO THE ANALYSIS OF STATIONARY NOISE AND SIGNALS CONTAMINATED WITH NOISE

Introduction

Noise Descriptors and Noise in Systems

Calculation of Noise Descriptors with Finite Discrete Data

Signal Averaging and Filtering for Signal-to-Noise Ratio Improvement

Introduction to the Application of Statistics and Information Theory to Genomics

Chapter Summary

BASIC MATHEMATICAL TOOLS USED IN THE CHARACTERIZATION OF PHYSIOLOGICAL SYSTEMS

Introduction

Some General Properties of Physiological Systems

Some Properties of Nonlinear Systems

Physical Factors Determining the Dynamic Behavior of Physiological Systems

Means of Characterizing Physiological Systems

Chapter Summary

INTRODUCTION TO THE MATHEMATICS OF TOMOGRAPHIC IMAGING

Introduction

Algebraic Reconstruction

The Radon Transform

The Fourier Slice Theorem

The Filtered Back-Projection Algorithm (FBPA)

Chapter Summary

APPENDICES

Cramer's Rule

Signal Flow Graphs and Mason's Rule

Bode (Frequency Response) Plots

Computational Tools for Biomedical Signal Processing and Systems Analysis

BIBLIOGRAPHY AND REFERENCES

INDEX

The interdisciplinary field of biomedical engineering requires its practitioners to master not only engineering skills, but also a diversity of material in the biological sciences. This text helps biomedical engineers strengthen their skills in the common network of applied mathematics that ties together these diverse disciplines. Based on the author's 30 years of experience in teaching as well as his personal research on neurosensory systems, Signals and Systems Analysis in Biomedical Engineering provides a ready source of information on those specialized mathematical techniques most useful in describing and analyzing biomedical signals, including ECG, EEG, blood pressure, biochemical spectrograms, and tomographic images.

Enriched with many examples that promote sound practical analysis, this book:

INTRODUCTION TO BIOMEDICAL SIGNALS AND SYSTEMS

General Characteristics of Biomedical Signals

General Properties of Physiological Systems

Chapter Summary

REVIEW OF LINEAR SYSTEMS THEORY

Linearity; Causality, Stationarity

Analog Systems

Systems Described by Sets of ODEs

Linear System Characterization

Discrete Systems and Signals

Stability of Systems

Chapter Summary

THE LAPLACE TRANSFORM AND ITS APPLICATIONS

Introduction

Properties of the Laplace Transform

Some Examples of Finding Laplace Transforms

The Inverse Laplace Transform

Applications of the Laplace Transform

Chapter Summary

FOURIER SERIES ANALYSIS OF PERIODIC SIGNALS

Introduction

Properties of the Fourier Series

Fourier Series Examples

Chapter Summary

THE CONTINUOUS FOURIER TRANSFORM

Introduction

Properties of the CFT

Analog-to-Digital Conversion and the Sampling Theorem

The Analytical Signal and the Hilbert Transform

The Modulation Transfer Function in Imaging

Chapter Summary

THE DISCRETE FOURIER TRANSFORM

Introduction

The CFT, ICFT, DFT and IDFT

Data Window Functions

The FFT

Chapter Summary

INTRODUCTION TO TIME-FREQUENCY ANALYSIS OF BIOMEDICAL SIGNALS

Introduction

The Short-term Fourier Transform (STFT)

Gabor and Adaptive Gabor Transform

Wigner-Ville & Pseudo-Wigner Transforms

Cohen's General Class of JTF Distributions

Introduction to JTFA Using Wavelets

Applications of JTF Analysis to Physiological Signals

JTFA Software

Chapter Summary

INTRODUCTION TO THE ANALYSIS OF STATIONARY NOISE AND SIGNALS CONTAMINATED WITH NOISE

Introduction

Noise Descriptors and Noise in Systems

Calculation of Noise Descriptors with Finite Discrete Data

Signal Averaging and Filtering for Signal-to-Noise Ratio Improvement

Introduction to the Application of Statistics and Information Theory to Genomics

Chapter Summary

BASIC MATHEMATICAL TOOLS USED IN THE CHARACTERIZATION OF PHYSIOLOGICAL SYSTEMS

Introduction

Some General Properties of Physiological Systems

Some Properties of Nonlinear Systems

Physical Factors Determining the Dynamic Behavior of Physiological Systems

Means of Characterizing Physiological Systems

Chapter Summary

INTRODUCTION TO THE MATHEMATICS OF TOMOGRAPHIC IMAGING

Introduction

Algebraic Reconstruction

The Radon Transform

The Fourier Slice Theorem

The Filtered Back-Projection Algorithm (FBPA)

Chapter Summary

APPENDICES

Cramer's Rule

Signal Flow Graphs and Mason's Rule

Bode (Frequency Response) Plots

Computational Tools for Biomedical Signal Processing and Systems Analysis

BIBLIOGRAPHY AND REFERENCES

INDEX

The interdisciplinary field of biomedical engineering requires its practitioners to master not only engineering skills, but also a diversity of material in the biological sciences. This text helps biomedical engineers strengthen their skills in the common network of applied mathematics that ties together these diverse disciplines. Based on the author's 30 years of experience in teaching as well as his personal research on neurosensory systems, Signals and Systems Analysis in Biomedical Engineering provides a ready source of information on those specialized mathematical techniques most useful in describing and analyzing biomedical signals, including ECG, EEG, blood pressure, biochemical spectrograms, and tomographic images.

Enriched with many examples that promote sound practical analysis, this book:

INTRODUCTION TO BIOMEDICAL SIGNALS AND SYSTEMS

General Characteristics of Biomedical Signals

General Properties of Physiological Systems

Chapter Summary

REVIEW OF LINEAR SYSTEMS THEORY

Linearity; Causality, Stationarity

Analog Systems

Systems Described by Sets of ODEs

Linear System Characterization

Discrete Systems and Signals

Stability of Systems

Chapter Summary

THE LAPLACE TRANSFORM AND ITS APPLICATIONS

Introduction

Properties of the Laplace Transform

Some Examples of Finding Laplace Transforms

The Inverse Laplace Transform

Applications of the Laplace Transform

Chapter Summary

FOURIER SERIES ANALYSIS OF PERIODIC SIGNALS

Introduction

Properties of the Fourier Series

Fourier Series Examples

Chapter Summary

THE CONTINUOUS FOURIER TRANSFORM

Introduction

Properties of the CFT

Analog-to-Digital Conversion and the Sampling Theorem

The Analytical Signal and the Hilbert Transform

The Modulation Transfer Function in Imaging

Chapter Summary

THE DISCRETE FOURIER TRANSFORM

Introduction

The CFT, ICFT, DFT and IDFT

Data Window Functions

The FFT

Chapter Summary

INTRODUCTION TO TIME-FREQUENCY ANALYSIS OF BIOMEDICAL SIGNALS

Introduction

The Short-term Fourier Transform (STFT)

Gabor and Adaptive Gabor Transform

Wigner-Ville & Pseudo-Wigner Transforms

Cohen's General Class of JTF Distributions

Introduction to JTFA Using Wavelets

Applications of JTF Analysis to Physiological Signals

JTFA Software

Chapter Summary

INTRODUCTION TO THE ANALYSIS OF STATIONARY NOISE AND SIGNALS CONTAMINATED WITH NOISE

Introduction

Noise Descriptors and Noise in Systems

Calculation of Noise Descriptors with Finite Discrete Data

Signal Averaging and Filtering for Signal-to-Noise Ratio Improvement

Introduction to the Application of Statistics and Information Theory to Genomics

Chapter Summary

BASIC MATHEMATICAL TOOLS USED IN THE CHARACTERIZATION OF PHYSIOLOGICAL SYSTEMS

Introduction

Some General Properties of Physiological Systems

Some Properties of Nonlinear Systems

Physical Factors Determining the Dynamic Behavior of Physiological Systems

Means of Characterizing Physiological Systems

Chapter Summary

INTRODUCTION TO THE MATHEMATICS OF TOMOGRAPHIC IMAGING

Introduction

Algebraic Reconstruction

The Radon Transform

The Fourier Slice Theorem

The Filtered Back-Projection Algorithm (FBPA)

Chapter Summary

APPENDICES

Cramer's Rule

Signal Flow Graphs and Mason's Rule

Bode (Frequency Response) Plots

Computational Tools for Biomedical Signal Processing and Systems Analysis

BIBLIOGRAPHY AND REFERENCES

INDEX

Enriched with many examples that promote sound practical analysis, this book:

INTRODUCTION TO BIOMEDICAL SIGNALS AND SYSTEMS

General Characteristics of Biomedical Signals

General Properties of Physiological Systems

Chapter Summary

REVIEW OF LINEAR SYSTEMS THEORY

Linearity; Causality, Stationarity

Analog Systems

Systems Described by Sets of ODEs

Linear System Characterization

Discrete Systems and Signals

Stability of Systems

Chapter Summary

THE LAPLACE TRANSFORM AND ITS APPLICATIONS

Introduction

Properties of the Laplace Transform

Some Examples of Finding Laplace Transforms

The Inverse Laplace Transform

Applications of the Laplace Transform

Chapter Summary

FOURIER SERIES ANALYSIS OF PERIODIC SIGNALS

Introduction

Properties of the Fourier Series

Fourier Series Examples

Chapter Summary

THE CONTINUOUS FOURIER TRANSFORM

Introduction

Properties of the CFT

Analog-to-Digital Conversion and the Sampling Theorem

The Analytical Signal and the Hilbert Transform

The Modulation Transfer Function in Imaging

Chapter Summary

THE DISCRETE FOURIER TRANSFORM

Introduction

The CFT, ICFT, DFT and IDFT

Data Window Functions

The FFT

Chapter Summary

INTRODUCTION TO TIME-FREQUENCY ANALYSIS OF BIOMEDICAL SIGNALS

Introduction

The Short-term Fourier Transform (STFT)

Gabor and Adaptive Gabor Transform

Wigner-Ville & Pseudo-Wigner Transforms

Cohen's General Class of JTF Distributions

Introduction to JTFA Using Wavelets

Applications of JTF Analysis to Physiological Signals

JTFA Software

Chapter Summary

INTRODUCTION TO THE ANALYSIS OF STATIONARY NOISE AND SIGNALS CONTAMINATED WITH NOISE

Introduction

Noise Descriptors and Noise in Systems

Calculation of Noise Descriptors with Finite Discrete Data

Signal Averaging and Filtering for Signal-to-Noise Ratio Improvement

Introduction to the Application of Statistics and Information Theory to Genomics

Chapter Summary

BASIC MATHEMATICAL TOOLS USED IN THE CHARACTERIZATION OF PHYSIOLOGICAL SYSTEMS

Introduction

Some General Properties of Physiological Systems

Some Properties of Nonlinear Systems

Physical Factors Determining the Dynamic Behavior of Physiological Systems

Means of Characterizing Physiological Systems

Chapter Summary

INTRODUCTION TO THE MATHEMATICS OF TOMOGRAPHIC IMAGING

Introduction

Algebraic Reconstruction

The Radon Transform

The Fourier Slice Theorem

The Filtered Back-Projection Algorithm (FBPA)

Chapter Summary

APPENDICES

Cramer's Rule

Signal Flow Graphs and Mason's Rule

Bode (Frequency Response) Plots

Computational Tools for Biomedical Signal Processing and Systems Analysis

BIBLIOGRAPHY AND REFERENCES

INDEX

Enriched with many examples that promote sound practical analysis, this book:

INTRODUCTION TO BIOMEDICAL SIGNALS AND SYSTEMS

General Characteristics of Biomedical Signals

General Properties of Physiological Systems

Chapter Summary

REVIEW OF LINEAR SYSTEMS THEORY

Linearity; Causality, Stationarity

Analog Systems

Systems Described by Sets of ODEs

Linear System Characterization

Discrete Systems and Signals

Stability of Systems

Chapter Summary

THE LAPLACE TRANSFORM AND ITS APPLICATIONS

Introduction

Properties of the Laplace Transform

Some Examples of Finding Laplace Transforms

The Inverse Laplace Transform

Applications of the Laplace Transform

Chapter Summary

FOURIER SERIES ANALYSIS OF PERIODIC SIGNALS

Introduction

Properties of the Fourier Series

Fourier Series Examples

Chapter Summary

THE CONTINUOUS FOURIER TRANSFORM

Introduction

Properties of the CFT

Analog-to-Digital Conversion and the Sampling Theorem

The Analytical Signal and the Hilbert Transform

The Modulation Transfer Function in Imaging

Chapter Summary

THE DISCRETE FOURIER TRANSFORM

Introduction

The CFT, ICFT, DFT and IDFT

Data Window Functions

The FFT

Chapter Summary

INTRODUCTION TO TIME-FREQUENCY ANALYSIS OF BIOMEDICAL SIGNALS

Introduction

The Short-term Fourier Transform (STFT)

Gabor and Adaptive Gabor Transform

Wigner-Ville & Pseudo-Wigner Transforms

Cohen's General Class of JTF Distributions

Introduction to JTFA Using Wavelets

Applications of JTF Analysis to Physiological Signals

JTFA Software

Chapter Summary

INTRODUCTION TO THE ANALYSIS OF STATIONARY NOISE AND SIGNALS CONTAMINATED WITH NOISE

Introduction

Noise Descriptors and Noise in Systems

Calculation of Noise Descriptors with Finite Discrete Data

Signal Averaging and Filtering for Signal-to-Noise Ratio Improvement

Introduction to the Application of Statistics and Information Theory to Genomics

Chapter Summary

BASIC MATHEMATICAL TOOLS USED IN THE CHARACTERIZATION OF PHYSIOLOGICAL SYSTEMS

Introduction

Some General Properties of Physiological Systems

Some Properties of Nonlinear Systems

Physical Factors Determining the Dynamic Behavior of Physiological Systems

Means of Characterizing Physiological Systems

Chapter Summary

INTRODUCTION TO THE MATHEMATICS OF TOMOGRAPHIC IMAGING

Introduction

Algebraic Reconstruction

The Radon Transform

The Fourier Slice Theorem

The Filtered Back-Projection Algorithm (FBPA)

Chapter Summary

APPENDICES

Cramer's Rule

Signal Flow Graphs and Mason's Rule

Bode (Frequency Response) Plots

Computational Tools for Biomedical Signal Processing and Systems Analysis

BIBLIOGRAPHY AND REFERENCES

INDEX

Enriched with many examples that promote sound practical analysis, this book:

INTRODUCTION TO BIOMEDICAL SIGNALS AND SYSTEMS

General Characteristics of Biomedical Signals

General Properties of Physiological Systems

Chapter Summary

REVIEW OF LINEAR SYSTEMS THEORY

Linearity; Causality, Stationarity

Analog Systems

Systems Described by Sets of ODEs

Linear System Characterization

Discrete Systems and Signals

Stability of Systems

Chapter Summary

THE LAPLACE TRANSFORM AND ITS APPLICATIONS

Introduction

Properties of the Laplace Transform

Some Examples of Finding Laplace Transforms

The Inverse Laplace Transform

Applications of the Laplace Transform

Chapter Summary

FOURIER SERIES ANALYSIS OF PERIODIC SIGNALS

Introduction

Properties of the Fourier Series

Fourier Series Examples

Chapter Summary

THE CONTINUOUS FOURIER TRANSFORM

Introduction

Properties of the CFT

Analog-to-Digital Conversion and the Sampling Theorem

The Analytical Signal and the Hilbert Transform

The Modulation Transfer Function in Imaging

Chapter Summary

THE DISCRETE FOURIER TRANSFORM

Introduction

The CFT, ICFT, DFT and IDFT

Data Window Functions

The FFT

Chapter Summary

INTRODUCTION TO TIME-FREQUENCY ANALYSIS OF BIOMEDICAL SIGNALS

Introduction

The Short-term Fourier Transform (STFT)

Gabor and Adaptive Gabor Transform

Wigner-Ville & Pseudo-Wigner Transforms

Cohen's General Class of JTF Distributions

Introduction to JTFA Using Wavelets

Applications of JTF Analysis to Physiological Signals

JTFA Software

Chapter Summary

INTRODUCTION TO THE ANALYSIS OF STATIONARY NOISE AND SIGNALS CONTAMINATED WITH NOISE

Introduction

Noise Descriptors and Noise in Systems

Calculation of Noise Descriptors with Finite Discrete Data

Signal Averaging and Filtering for Signal-to-Noise Ratio Improvement

Introduction to the Application of Statistics and Information Theory to Genomics

Chapter Summary

BASIC MATHEMATICAL TOOLS USED IN THE CHARACTERIZATION OF PHYSIOLOGICAL SYSTEMS

Introduction

Some General Properties of Physiological Systems

Some Properties of Nonlinear Systems

Physical Factors Determining the Dynamic Behavior of Physiological Systems

Means of Characterizing Physiological Systems

Chapter Summary

INTRODUCTION TO THE MATHEMATICS OF TOMOGRAPHIC IMAGING

Introduction

Algebraic Reconstruction

The Radon Transform

The Fourier Slice Theorem

The Filtered Back-Projection Algorithm (FBPA)

Chapter Summary

APPENDICES

Cramer's Rule

Signal Flow Graphs and Mason's Rule

Bode (Frequency Response) Plots

Computational Tools for Biomedical Signal Processing and Systems Analysis

BIBLIOGRAPHY AND REFERENCES

INDEX