Signals and systems analysis in biomedical engineering

656 Pages·2011·15.172 MB·English

by  Northrop, Robert B

SIGNALS and SYSTEMS
ANALYSIS in BIOMEDICAL
ENGINEERING
Second Edition
(cid:52)(cid:80)(cid:74)(cid:79)(cid:72)(cid:76)(cid:83)(cid:3)(cid:57)(cid:21)(cid:3)(cid:53)(cid:76)(cid:92)(cid:84)(cid:72)(cid:85)(cid:19)(cid:3)(cid:58)(cid:76)(cid:89)(cid:80)(cid:76)(cid:90)(cid:3)(cid:44)(cid:75)(cid:80)(cid:91)(cid:86)(cid:89)
Published Titles
Electromagnetic Analysis and Design in Magnetic Resonance Imaging,
Jianming Jin
Endogenous and Exogenous Regulation and Control of Physiological
Systems, Robert B. Northrop
Artificial Neural Networks in Cancer Diagnosis, Prognosis, and
Treatment, Raouf N.G. Naguib and Gajanan V. Sherbet
Medical Image Registration, Joseph V. Hajnal, Derek Hill,
and David J. Hawkes
Introduction to Dynamic Modeling of Neuro-Sensory Systems,
Robert B. Northrop
Noninvasive Instrumentation and Measurement in Medical Diagnosis,
Robert B. Northrop
Handbook of Neuroprosthetic Methods, Warren E. Finn
and Peter G. LoPresti
Angiography and Plaque Imaging: Advanced Segmentation
Techniques, Jasjit S. Suri and Swamy Laxminarayan
Analysis and Application of Analog Electronic Circuits to Biomedical
Instrumentation, Robert B. Northrop
Biomedical Image Analysis, Rangaraj M. Rangayyan
An Introduction to Biomaterials, Scott A. Guelcher
and Jeffrey O. Hollinger
Foot and Ankle Motion Analysis: Clinical Treatment and Technology,
Gerald F. Harris, Peter A. Smith, Richard M. Marks
Introduction to Molecular Biology, Genomics and Proteomic for
Biomedical Engineers, Robert B. Northrop and Anne N. Connor
Signals and Systems Analysis in Biomedical Engineering,
Second Edition, Robert B. Northrop
Michael R. Neuman, Series Editor
Robert B. Northrop
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
MATLAB® and Simulink® are trademarks of the MathWorks, Inc. and are used with permission. The Math-
Works does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion
of MATLAB® and Simulink® software or related products does not constitute endorsement or sponsorship
by the MathWorks of a particular pedagogical approach or particular use of the MATLAB®and Simulink®
software.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2010 by Taylor and Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed in the United States of America on acid-free paper
10 9 8 7 6 5 4 3 2 1
International Standard Book Number-13: 978-1-4398-1253-2 (Ebook-PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has
not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit-
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the CCC,
a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used
only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
About the Author ...............................................................................................................ix
1 Introduction to Biomedical Signals and Systems
1.1 General Characteristics of Biomedical Signals .............................................1-2
1.2 General Properties of PSs ...............................................................................1-21
1.3 Chapter Summary ...........................................................................................1-24
2 Review of Linear Systems Theory
2.1 Linearity, Causality, and Stationarity .............................................................2-1
2.2 Analog Systems ..................................................................................................2-2
2.3 Systems Described by Sets of ODEs ..............................................................2-10
2.4 Linear System Characterization ....................................................................2-21
2.5 Discrete Signals and Systems .........................................................................2-39
2.6 Stability of Systems ..........................................................................................2-61
2.7 Chapter Summary ...........................................................................................2-63
3 The Laplace Transform and Its Applications
3.1 Introduction .......................................................................................................3-1
3.2 Properties of the Laplace Transform ..............................................................3-3
3.3 Some Examples of Finding Laplace Transforms ..........................................3-5
3.4 The Inverse Laplace Transform .......................................................................3-6
3.5 Applications of the Laplace Transform ..........................................................3-7
3.6 Chapter Summary ...........................................................................................3-19
4 Fourier Series Analysis of Periodic Signals
4.1 Introduction .......................................................................................................4-1
4.2 Properties of the FS ...........................................................................................4-3
4.3 FS Examples ........................................................................................................4-4
4.4 Chapter Summary .............................................................................................4-9
5 The Continuous Fourier Transform
5.1 Introduction .......................................................................................................5-1
5.2 Properties of the CFT ........................................................................................5-2
vi Contents
5.3 ADC and the Sampling Theorem ....................................................................5-5
5.4 The Analytical Signal and the HT...................................................................5-8
5.5 MTF in Imaging ...............................................................................................5-18
5.6 Chapter Summary ...........................................................................................5-25
6 The Discrete Fourier Transform
6.1 Introduction .......................................................................................................6-1
6.2 The CFT, ICFT, DFT, and IDFT ......................................................................6-2
6.3 Data Window Functions ...................................................................................6-7
6.4 The FFT .............................................................................................................6-13
6.5 Chapter Summary ...........................................................................................6-21
7 Introduction to Joint Time-Frequency Analysis
of Biomedical Signals
7.1 Introduction .......................................................................................................7-1
7.2 The Short-Term Fourier Transform ................................................................7-4
7.3 The Gabor and Adaptive Gabor Transforms .................................................7-6
7.4 The Wigner–Ville and Pseudo-Wigner Transforms ....................................7-7
7.5 Cohen’s General Class of JTF Distributions ................................................7-11
7.6 Introduction to JTFA Using Wavelets ..........................................................7-14
7.7 Applications of JTFA to Physiological Signals ............................................7-21
7.8 JTFA Software ..................................................................................................7-32
7.9 Chapter Summary ...........................................................................................7-34
8 Introduction to the Analysis of Stationary Noise
and Signals Contaminated with Noise
8.1 Introduction .......................................................................................................8-1
8.2 Noise Descriptors and Noise in Systems ........................................................8-2
8.3 Calculation of Noise Descriptors with Finite Discrete Data ....................8-30
8.4 Signal Averaging and Filtering for SNR Improvement..............................8-32
8.5 Introduction to the Application of Statistics and IT to Genomics .........8-46
8.6 Chapter Summary ..........................................................................................8-66
9 Basic Mathematical Tools Used in the Characterization
of Physiological Systems
9.1 Introduction .......................................................................................................9-1
9.2 Some General Properties of PSs ......................................................................9-1
9.3 Some Properties of Nonlinear Systems ..........................................................9-5
9.4 Physical Factors Determining the Dynamic Behavior of PSs ....................9-7
9.5 Means of Characterizing PSs .........................................................................9-14
9.6 Chapter Summary ..........................................................................................9-40
10 Introduction to the Mathematics of Tomographic Imaging
10.1 Introduction .....................................................................................................10-1
10.2 Algebraic Reconstruction ...............................................................................10-5
10.3 The Radon Transform .....................................................................................10-8
10.4 The Fourier Slice Theorem ...........................................................................10-14
Contents vii
10.5 Filtered Back-Projection Algorithm ..............................................................10-15
10.6 Chapter Summary ............................................................................................10-18
11 Introduction to the Analysis of Nonlinear Biochemical
Systems and Biochemical Oscillators
11.1 Introduction: Some General Properties of Nonlinear Systems ................11-1
11.2 All Living Systems Are Nonlinear ................................................................11-8
11.3 Parametric Regulation in Nonlinear Biological Systems ..........................11-8
11.4 Approaches to Nonlinear Analysis: The Phase Plane ..............................11-14
11.5 Chaos, Stability, and Limit Cycles in Nonlinear Biological Systems .....11-19
11.6 Chapter Summary .........................................................................................11-66
12 Introduction to Complex Systems in Biology and Medicine
12.1 Introduction to Complex Systems ................................................................12-1
12.2 When Is a System Complex? ..........................................................................12-2
12.3 Some Examples ................................................................................................12-3
12.4 Properties of Complex Systems: Chaos and Tipping Points .....................12-4
12.5 The Law of Unintended Consequences .......................................................12-6
12.6 Why Study Complex Systems? .......................................................................12-9
12.7 Human Responses to Complexity ...............................................................12-10
12.8 Complex Systems Engineering ....................................................................12-13
12.9 Some Complex Physiological Regulatory Systems ...................................12-15
12.10 Structure and Function: Some Examples of Complex Physiological
Regulatory Systems and Their Simplified Models ....................................12-21
12.11 Examples of When Complex Physiological Systems Fail ........................12-78
12.12 Some Approaches to Dealing with Complexity in an Organized
Manner ...........................................................................................................12-86
12.13 Chapter Summary .........................................................................................12-93
Appendix A .....................................................................................................Appendix A-1
Appendix B .....................................................................................................Appendix B-1
Appendix C .....................................................................................................Appendix C-1
Appendix D .....................................................................................................Appendix D-1
Glossary ..................................................................................................................Glossary-1
Bibliography ................................................................................................Bibliography-1
Index ..............................................................................................................................Index-1

About the Author
Robert B. Northrop was born in White Plains, NY, in 1935. After graduating from
Staples High School in Westport, CT, he majored in electrical engineering (EE) at the
Massachusetts Institute of Technology, graduating with a bachelor’s degree in 1956. At
the University of Connecticut (UCONN), he received a master’s degree in systems engi-
neering in 1958. As the result of a long-standing interest in physiology, he entered a PhD
program at UCONN in physiology, doing research on the neuromuscular physiology of
molluskan catch muscles. He received his PhD in 1964.
In 1963, he rejoined the UCONN EE department as a lecturer, and was hired as an
assistant professor of EE in 1964. In collaboration with his PhD advisor, Dr. Edward
G. Boettiger, he secured a 5-year training grant in 1965 from the National Institute of
General Medical Sciences [National Institutes of Health (NIH)], and started one of the
first, interdisciplinary, biomedical engineering (BME) graduate training programs in
New England. UCONN currently awards MS and PhD degrees in this field of study, as
well as BS degrees in engineering under the BME area of concentration.
Throughout his career, Dr. Northrop’s research interests have been broad and inter-
disciplinary and have been centered on BME. He has conducted sponsored research on
the neurophysiology of insect and frog vision and devised theoretical models for visual
neural signal processing. He has also conducted sponsored research on electrofishing
and developed, in collaboration with Northeast Utilities, effective, working systems for
fish guidance and control in hydroelectric plant waterways on the Connecticut River at
Holyoke, MA, using underwater electric fields.
Another area of his sponsored research has been in the design and simulation of
nonlinear, adaptive, digital controllers to regulate in vivo drug concentrations or physi-
ological parameters, such as pain, blood pressure, or blood glucose in diabetics. An out-
growth of this research has led him to develop mathematical models for the dynamics
of the human immune system, which were used to investigate theoretical therapies for
autoimmune diseases, cancer, and human immunodeficiency virus infection.
Biomedical instrumentation has also been an active research area for Dr. Northrop
and his graduate students: an NIH grant–supported study on the use of the ocular pulse
to detect obstructions in the carotid arteries. Minute pulsations of the cornea from arte-
rial circulation in the eyeball were sensed using a no-touch, phase-locked, ultrasound
ix