Table Of ContentThis is a volume in the
ACADEMIC PRESS SERIES IN BIOMEDICAL ENGINEERING
JOSEPH BRONZINO, SERIES EDITOR
TRINITY COLLEGEdHARTFORD, CONNECTICUT
CIRCUITS,
SIGNALS, AND
SYSTEMS FOR
BIOENGINEERS
A MATLAB(cid:1)-BASED
INTRODUCTION
THIRD EDITION
J S
OHN EMMLOW
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Dedicated to
Susanne Oldham
Who has shown me, and shared with me, so much of life.
Let the adventure continue.
Preface to the Third Edition
This edition was motivated in large part filters,theirimportancein signalprocessing
by the continuously changing educational justifies introducing the z-transform before
environment in biomedical engineering. describing digital filters. Finally, a more
The wide-ranging expertise expected of a traditional approach is followed in this
competent biomedical engineer continues to editioninwhichtime-domainconceptssuch
grow, putting additional stress on curricula as convolution are presented before intro-
and courses. This text provides a compre- ducing frequency-domain analyses.
hensive introductory coverage of linear Many biomedical engineering programs
systems,includingcircuitanalysis.Notallof covercircuitsinaseparatecourse(usuallyin
the material can be covered in a single 3-h electricalengineering). Yettheremaycomea
course; rather the book is designed to allow timewhenprogramsincludethismaterial,so
the instructorto choosethose topicsdeemed asectiononcircuitsremainsattheendofthe
most essentialandto beableto find themin book.Chapter15onelectronicsisnotusually
a single, coherent text. includedinalinearsystemscourse,butsince
the students will have the necessary back-
groundtoanalyzeusefulcircuits,Ithoughtit
NEW TO THIS EDITION
worth including. Not all instructors will
choose to include these new topics, but they
The third edition presents a number of are relevant and I feel they should be avail-
modifications over the previous text pri- able as options. The chapters on circuits also
marily in the form of new material. Each include sections on lumped-parameter me-
chapternowbeginswithasectiondescribing chanical systems that should be considered
andlistingthegoalsofthatchapterandends optional.
with a summary of topics covered. In addi- Retained from earlier editions is the
(cid:1)
tion, several new chapters have been added. strongrelianceonMATLAB .Thissoftware
Noise is ubiquitous in biomedical mea- is an essential adjunct to understanding
surements and nonlinearity is inherent in signals and systems, and this book is not
most biomedical systems. These important meant to be used without this powerful
measurement features required a new pedagogical tool. Another concept from
chapter on stochastic, nonstationary, and earlier editions is the development of some
nonlinearsystemsandsignals.Achapteron of the deeper concepts, such as the Fourier
basic image analysis has been added along transform and the transfer function, using
with introductory material. This chapter an intuitive approach. For example, the
extends some one-dimensional signal pro- Fourier transform is presented in the
cessing tools to two dimensions. Although context of correlation between an unknown
the only discrete systems a biomedical signal and a family of sinusoidal probing
engineer is likely to encounter are digital functions.
xi
xii
PREFACETOTHETHIRDEDITION
The general philosophy of this text is to given in the book. Since many of the prob-
introduce and develop concepts through lems are extensions or modifications of
computational methods that allow students examples, these files can be helpful in
to explore operations such as correlations, reducing the amount of typing required to
convolution, the Fourier transform, and the carry out an assignment. Please visit www.
transfer function. I also include a few ex- elsevierdirect.com, search on “Semmlow,”
amples and problems that follow more select the link to “Circuits, Signals, and
traditionalmethodsofmathematicalrigor.A Systems forBioengineers-3rdEdition,”and
few more intriguing problems have been click on the “companion site” link on the
sprinkled into the problem sets for added book’s web page to download this material.
interest and challenge, and many more For instructors, an educational support
problems are now based on biological package is available that contains a set of
examples. PowerPoint files that include all of the
figuresandmostoftheequationsalongwith
supporting text for each chapter. This
ANCILLARIES
package also contains the solutions to the
problem sets and some sample examina-
The text comes with a number of educa- tions.Thepackageisavailablefordownload
tional support materials. For purchasers of from the publisher at: www.textbooks.
the text, a website contains downloadable elsevier.com.
(cid:1)
data and MATLAB functions needed to
(cid:1)
solvetheproblems,afewhelpfulMATLAB John L. Semmlow, PhD
(cid:1)
routines, and all of the MATLAB examples New Brunswick, NJ 2017
Acknowledgments
This text benefited from comments and University; and Ana Paula Rocha, Assistant
ideas from several biomedical engineering ProfessorofMathematicsattheUniversityof
educators from across the globe. I am partic- Porto, Portugal. Three graduate students in
ularlygratefultoRebecaGoyaEstebaninthe the Department of Biomedical Engineering
DepartmentofSignalTheoryandCommuni- atRutgersUniversityassistedwiththeediting
cationofReyJuanCarlosUniversity,Madrid, ofthe manuscript: Cosmas Mwikirize,Hwan
whocarefullyreviewedanumberofchapters June Kang, and Matthew Richtmyer. Despite
and offered advice, corrections, and sugges- their help, I suspect some errors still slipped
tions.Iwouldalsoliketorecognizecontribu- through for which I am exclusively to be
tions and suggestions from Hananeh blamed.Finally,Iwanttoexpressmythanks
Esmailbeigi, Clinical Assistant Professor, to Susanne Oldham (to whom this book is
Department of Bioengineering at the Univer- dedicated)forherpatienteditingandsupport
sity of Illinois at Chicago (one of my former andtoPeggyChristwhodemonstratedgreat
hangouts);YongK.Kim,ChancellorProfessor understandingduringthefartoolongprepa-
of Bioengineering at UMass Dartmouth; rationofthisbook.
Hatice Ozturk, Teaching Associate Professor
of Electrical, Computer and Biomedical John L. Semmlow, PhD
Engineering at North Carolina State New Brunswick, NJ, 2017
xiii
C H A P T E R
1
The Big Picture: Bioengineering
Signals and Systems
1.1 WHY BIOMEDICAL ENGINEERS NEED TO ANALYZE SIGNALS
AND SYSTEMS
Withonlyslightexaggeration,justabouteverythingweencountercanbecalledasystem.
Partofthisisduetothebroaddefinitionofasystem:acollectionofprocessesorcomponents
thatinteractwithacommonpurpose.Inthisbook,weareinterestedinsignalsaswellassys-
tems,soforourpurposesasystemisdefinedasacollectionofprocessesorcomponentsthat
operateon,ororiginate,oneormoresignals.Thehumanbodyoffersmanyexamplesofwell-
definedsystems devotedtoacommonpurpose.Thecardiovascularsystemdeliversoxygen-
carrying blood to the peripheral tissues. The pulmonary system is devoted to exchanging
gases (primarily O and CO ) between the blood and air. The mission of the renal system
2 2
is to regulate water and ion balance and adjust the concentration of ions and molecules.
Mass communication is the objective of the endocrine system with the distribution of
signalingmoleculesthrough thebloodstream,whereasthenervous system performstightly
controlled communication using neurons and axons to process and transmit information
coded as electrical impulses.
Many medical specialties, particularly areas of internal medicine, emphasize a specific
physiological system. Cardiologists specialize in the cardiovascular system, neurologists in
thenervoussystem,ophthalmologistsinthevisualsystem,nephrologistsinthekidneys,pul-
monologistsintherespiratorysystem,gastroenterologistsinthedigestivesystem,andendo-
crinologists in the endocrine system. Most other medical specialties are based on common
tools or approaches such as surgery, radiology, and anesthesiology, whereas one specialty,
pediatrics, is based on the type of patient.
Given this systems-based approach to physiology and medicine, it is not surprising that
early bioengineers applied their engineering tools to some of these systems. Early applica-
tionsofsystemsanalysisincludedthequantificationandexplanationoftheoscillatoryrespi-
ratory patterns known as CheyneeStokes respiration, understanding the neural control
factors underlying the speed and accuracy of the eye movements, and explaining the mech-
anismofpupiloscillationscalledhippus.Thenervoussystem,withitsapparentsimilarityto
Circuits,Signals,andSystemsforBioengineers 3
http://dx.doi.org/10.1016/B978-0-12-809395-5.00001-1 Copyright©2018ElsevierInc.Allrightsreserved.
4
1. THEBIGPICTURE:BIOENGINEERINGSIGNALSANDSYSTEMS
early computers, was another favorite target of bioengineers, as was the cardiovascular sys-
tem with its obvious links to hydraulics and fluid dynamics. Some of these early efforts are
describedinthesectionsonsystemandanalogmodels.Asbioengineeringhasexpandedinto
areasofmolecularbiology,systemsonthecellular,andevensubcellular,levelshaveutilized
the tool of system analysis.
Irrespectiveofthetypeofbiologicalsystem,itneedstointeractwithothersystemsandwe
bioengineers need a way of interacting with these systems. Signals, or more specifically
“biosignals,” carry information and mediate this intrasystem communication. By definition,
signals carry information that we can use; if a “signal” contains no useful information, it is
“noise.”1 (Quotes are used to highlight terms that are particularly important and should be
an integral part of a bioengineer’s vocabulary.) Physicians and biomedical researchers
(who can be viewed as large, complex systems) use the information contained in biosignals
todetermineordiagnosethestateofaphysiologicalsystem.Suchbiosignalsariseaschanges
in various biological or physiological variables. Common signals measured in diagnostic
medicine include: electrical activity of the heart, muscles, and brain; blood pressure; heart
rate; blood gas concentrations and concentrations of other blood components; and sounds
generated by the heart and its valves.
Often, it isdesirable to send signalsinto a biological systemforpurposes of experimenta-
tionortherapy.Weoftenusetheterm“stimulus”forsignalsdirectedataspecificphysiolog-
ical system; if an output signal is evoked by these inputs, we term it a “response.” In this
scenario, the biological system acts like an inputeoutput system, a classic model used in
systems analysis and illustrated in Figure 1.1.
Examplesofwell-definedinputeoutputphysiologicalsystemsincludetheknee-jerkreflex,
wheretheinputisamechanicalforceandtheoutputismechanicalmotion,andthepupillary
lightreflex,wheretheinputislightandtheoutputisamechanicalchangeintheirismuscles.
Drug treatments can be included in this inputeoutput description, where the input is the
molecular configuration of the drug and the output is the therapeutic benefit (if any). Such
system-analytic representations are further explored in the sections on systems and analog
modeling.
Systemsthatproduceanoutputwithouttheneedforaninputstimulus,liketheelectrical
activity of the heart, are considered biosignal “sources.” (Although the electrical activity of
the heart can be moderated by stimuli, such as exercise, the basic signal does not require a
specific stimulus.) Input-only systems, like write-only memory, are not very useful since
the purpose of an input signal is usually to produce some sort of response. An exception
FIGURE1.1
Aclassicsystemsviewofaphysiologicalsystemthatreceivesanexternalstimulusorinputsignal
thatevokesaresponseoroutput.
1Wesometimesusetheterm“randomsignal”whichisasignalthatdoesnotcarryinformation,soitreally
shouldbecalled“randomnoise.”Putthisdowntosloppyterminologyandjustsubstitute“noise”for“signal”
whenyouseeit.
I. SIGNALS
5
1.1 WHYBIOMEDICALENGINEERSNEEDTOANALYZESIGNALSANDSYSTEMS
is the placebo, which is designed to produce no physiological response. (Nonetheless, it
sometimes produces substantive results probably by interacting through complex, poorly
understood neurological processes.)
Sinceallofourinteractionswithphysiologicalsystemsarethroughbiosignals,thecharac-
teristics of these signals are of great importance. Gleaning more information from these sig-
nals with signal processing tools is also very important in bioengineering. Indeed, much of
modern medical technology is devoted to either extracting new physiological signals from
the body or gaining more information from existing biosignals.
1.1.1 Goals of This Book
ThetoolsofMATLABmakeitpossibleforbioengineerstobetteranalyzeandunderstand
signals and systems, the bread and butter of our professional lives. This book helps you to
make the most of this powerful computer language in its applications to signal processing
and systems analysis. The objective of this book is to give the reader a fundamental under-
standing of the field traditionally known as “linear systems analysis,” but with concepts
andapplications inbioengineering. The basicideasoflinear systems analysisarewellestab-
lished and well understood. They can be divided into areas of signal analysis, system anal-
ysis, and the application of systems to signals known as signal processing.
The goal of signal analysis is to extract information from a signal by identifying features
that are of particular interest. This includes basic and refined descriptions of a signal’s
time representation and a breakdown of its frequency content. This book covers the how
and why of examining the correlations that occur between different portions of a signal.
We find that correlation isausefultoolin signal analysis:we useit to determine similarities
betweentwosignals.Whenweusecorrelationtocompareasignalandthe(almostmystical)
sinusoidalwaveform,wediscoverthatabunchofsinusoidscangiveanalternative,yetcom-
plete representation of almost any signal. Moreover, applying a little algebra to this alterna-
tive“sinusoidal”representationcangiveusthe“frequencyspectrum”(orjust“spectrum”)of
the signal.
Insystemsanalysis,thebasicgoalistobeabletodescribe,quantitatively,theresponseofa
systemtoawidevarietyofstimuli.Wewillfirstlearntodefinesystembehavioranalytically
using differential equations. However, as is typical of engineers, we will find an easy way
solve these equations using algebra. When digital systems are involved, they are described
usingdifferenceequationratherthandifferentialequations,butagainwesolvethemalgebra-
ically.Surpassingthesetraditionalanalysismethodsineaseandpoweriscontinuoussystem
simulation implemented here with MATLAB’s powerful system simulation tool, Simulink.
Thistoolallowsustodescribethebehaviorofverycomplexsystems,eventhosethatinclude
nonlinear elements.
Mixingsignalandsystemanalysis,weusesomespecialsystemstoaltersignals.Applying
these systems to a signal can produce an altered signal that is more useful to us. Often this
increasedutilityisachievedbyremovingdistractingcomponentsfromthesignal(i.e.,noise).
Forexample,wemightremovefrequenciesinthesignalthatdonotcontributetothesignal’s
informationcontent.Usingasystemtoremoveunwantedfrequenciesisknownas“filtering”
and the special system that does this is called, logically, a filter.
I. SIGNALS
