Signals and Systems(4)

signal and system 英文原版书Title: An Overview of the Book "Signal and System"Introduction:The book "Signal and System" is an essential resource for anyone interested in understanding the fundamentals of signal processing and system analysis. It provides a comprehensive and in-depth exploration of the concepts, theories, and applications related to signals and systems. This article aims to provide a detailed overview of the book, highlighting its key points and relevance.I. Fundamental Concepts of Signals and Systems:1.1 Definition and Properties of Signals:- Explanation of signals as time-varying or spatially varying quantities.- Discussion on continuous-time and discrete-time signals.- Description of signal properties such as amplitude, frequency, and phase.1.2 Classification of Signals:- Overview of different types of signals including periodic, aperiodic, deterministic, and random signals.- Explanation of energy and power signals.- Introduction to common signal operations such as time shifting, scaling, and time reversal.1.3 System Classification and Properties:- Definition and classification of systems as linear or nonlinear, time-invariant or time-varying.- Explanation of system properties like causality, stability, and linearity.- Introduction to system representations such as differential equations, transfer functions, and state-space models.II. Time-Domain Analysis of Signals and Systems:2.1 Convolution and Correlation:- Detailed explanation of convolution and its significance in system analysis.- Discussion on correlation as a measure of similarity between signals.- Application of convolution and correlation in practical scenarios.2.2 Fourier Series and Transform:- Introduction to Fourier series and its representation of periodic signals.- Explanation of Fourier transform and its application in analyzing non-periodic signals.- Discussion on the properties of Fourier series and transform.2.3 Laplace Transform:- Overview of Laplace transform and its use in solving differential equations.- Explanation of the relationship between Laplace transform and frequency response of systems.- Application of Laplace transform in system analysis and design.III. Frequency-Domain Analysis of Signals and Systems:3.1 Frequency Response:- Definition and interpretation of frequency response.- Explanation of magnitude and phase response.- Analysis of frequency response using Bode plots.3.2 Filtering and Filtering Techniques:- Introduction to digital and analog filters.- Discussion on different filter types such as low-pass, high-pass, band-pass, and band-stop filters.- Explanation of filter design techniques including Butterworth, Chebyshev, and Elliptic filters.3.3 Sampling and Reconstruction:- Explanation of sampling theorem and its importance in signal processing.- Overview of sampling techniques and their impact on signal reconstruction.- Discussion on anti-aliasing filters and reconstruction methods.IV. System Analysis and Stability:4.1 System Response and Impulse Response:- Explanation of system response to different input signals.- Introduction to impulse response and its relationship with system behavior.- Analysis of system stability based on impulse response.4.2 Transfer Function and Frequency Domain Analysis:- Definition and interpretation of transfer function.- Explanation of frequency domain analysis using transfer function.- Application of transfer function in system design and analysis.4.3 Feedback Systems and Control:- Overview of feedback systems and their role in control theory.- Explanation of stability analysis and design using control theory.- Discussion on PID controllers and their applications.V. Applications of Signal and System Theory:5.1 Communication Systems:- Explanation of modulation techniques and their role in communication systems.- Overview of demodulation techniques and their significance.- Discussion on error control coding and channel equalization.5.2 Digital Signal Processing:- Introduction to digital signal processing and its applications.- Explanation of digital filters and their role in signal processing.- Overview of image and speech processing techniques.5.3 Signal Processing in Biomedical Engineering:- Application of signal processing in biomedical signal analysis.- Discussion on medical imaging techniques such as MRI and CT scans.- Explanation of signal processing methods used in ECG and EEG analysis.Conclusion:The book "Signal and System" provides a comprehensive and detailed exploration of the fundamental concepts, theories, and applications related to signals and systems. It covers a wide range of topics including signal classification, system analysis, frequency-domain analysis, stability, and various applications. By studying this book, readers can gain a solid understanding of signal and system theory, which is essential in various fields such as communication, digital signal processing, and biomedical engineering.。

信号与系统目录（Signal and system directory）Chapter 1 signals and systems1.1 INTRODUCTION1.2 signalContinuous signals and discrete signalsTwo. Periodic signals and aperiodic signalsThree, real signal and complex signalFour. Energy signal and power signalThe basic operation of 1.3 signalAddition and multiplicationTwo, inversion and TranslationThree, scale transformation (abscissa expansion)1.4 step function and impulse functionFirst, step function and impulse functionTwo. Definition of generalized function of impulse functionThree. The derivative and integral of the impulse functionFour. Properties of the impulse functionDescription of 1.5 systemFirst, the mathematical model of the systemTwo. The block diagram of the systemCharacteristics and analysis methods of 1.6 systemLinearTwo, time invarianceThree, causalityFour, stabilityOverview of five and LTI system analysis methodsExercise 1.32The second chapter is the time domain analysis of continuous systemsThe response of 2.1LTI continuous systemFirst, the classical solution of differential equationTwo, about 0- and 0+ valuesThree, zero input responseFour, zero state responseFive, full response2.2 impulse response and step responseImpulse responseTwo, step response2.3 convolution integralConvolution integralTwo. The convolution diagramThe properties of 2.4 convolution integralAlgebraic operations of convolutionTwo. Convolution of function and impulse function Three. Differential and integral of convolutionFour. Correlation functionExercise 2.34The third chapter is the time domain analysis of discretesystemsThe response of 3.1LTI discrete systemsDifference and difference equationsTwo. Classical solutions of difference equationsThree, zero input responseFour, zero state response3.2 unit sequence and unit sequence responseUnit sequence and unit step sequenceTwo, unit sequence response and step response3.3 convolution sumConvolution sumTwo. The diagram of convolution sumThree. The nature of convolution sum3.4 deconvolutionExercise 3.27The fourth chapter is Fourier transform and frequency domainanalysis of the systemThe 4.1 signal is decomposed into orthogonal functions Orthogonal function setTwo. The signal is decomposed into orthogonal functions 4.2 Fourier seriesDecomposition of periodic signalsTwo, Fourier series of odd even functionThree. Exponential form of Fu Liye seriesThe spectrum of 4.3 period signalFrequency spectrum of periodic signalTwo, the spectrum of periodic matrix pulseThree. The power of periodic signal4.4 the spectrum of aperiodic signalsFirst, Fu Liye transformTwo. Fourier transform of singular functionsProperties of 4.5 Fourier transformLinearTwo, parityThree, symmetryFour, scale transformationFive, time shift characteristicsSix, frequency shift characteristicsSeven. Convolution theoremEight, time domain differential and integral Nine, frequency domain differential and integral Ten. Correlation theorem4.6 energy spectrum and power spectrumEnergy spectrumTwo. Power spectrumFourier transform of 4.7 periodic signals Fourier transform of sine and cosine functionsTwo. Fourier transform of general periodic functionsThree 、 Fu Liye coefficient and Fu Liye transformFrequency domain analysis of 4.8 LTI systemFrequency responseTwo. Distortionless transmissionThree. The response of ideal low-pass filter4.9 sampling theoremSampling of signalsTwo. Time domain sampling theoremThree. Sampling theorem in frequency domainFourier analysis of 4.10 sequencesDiscrete Fourier series DFS of periodic sequencesTwo. Discrete time Fourier transform of non periodic sequences DTFT4.11 discrete Fu Liye and its propertiesDiscrete Fourier transform (DFT)Two. The properties of discrete Fourier transformExercise 4.60The fifth chapter is the S domain analysis of continuous systems 5.1 Laplasse transformFirst, from Fu Liye transform to Laplasse transformTwo. Convergence domainThree, (Dan Bian) Laplasse transformThe properties of 5.2 Laplasse transformLinearTwo, scale transformationThree, time shift characteristicsFour, complex translation characteristicsFive, time domain differential characteristicsSix, time domain integral characteristicsSeven. Convolution theoremEight, s domain differential and integralNine, initial value theorem and terminal value theorem5.3 Laplasse inverse transformationFirst, look-up table methodTwo, partial fraction expansion method5.4 complex frequency domain analysisFirst, the transformation solution of differential equation Two. System functionThree. The s block diagram of the systemFour 、 s domain model of circuitFive, Laplasse transform and Fu Liye transform5.5 bilateral Laplasse transformExercise 5.50The sixth chapter is the Z domain analysis of discrete systems 6.1 Z transformFirst, transform from Laplasse transform to Z transformTwo, z transformThree. Convergence domainProperties of 6.2 Z transformLinearTwo. Displacement characteristicsThree, Z domain scale transformFour. Convolution theoremFive, Z domain differentiationSix, Z domain integralSeven, K domain inversionEight, part sumNine, initial value theorem and terminal value theorem 6.3 inverse Z transformFirst, power series expansion methodTwo, partial fraction expansion method6.4 Z domain analysisThe Z domain solution of difference equationTwo. System functionThree. The Z block diagram of the systemFour 、 the relation between s domain and Z domainFive. Seeking the frequency response of discrete system by means of DTFTExercise 6.50The seventh chapter system function7.1 system functions and system characteristicsFirst, zeros and poles of the system functionTwo. System function and time domain responseThree. System function and frequency domain responseCausality and stability of 7.2 systemsFirst, the causality of the systemTwo, the stability of the system7.3 information flow graphSignal flow graphTwo, Mason formulaStructure of 7.4 systemFirst, direct implementationTwo. Implementation of cascade and parallel connectionExercise 7.39The eighth chapter is the analysis of the state variables of the system8.1 state variables and state equationsConcepts of state and state variablesTwo. State equation and output equationEstablishment of state equation for 8.2 continuous systemFirst, the equation is directly established by the circuit diagramTwo. The equation of state is established by the input-output equationEstablishment and Simulation of state equations for 8.3discrete systemsFirst, the equation of state is established by the input-output equationTwo. The system simulation is made by the state equationSolution of state equation of 8.4 continuous systemFirst, the Laplasse transform method is used to solve the equation of stateTwo, the system function matrix H (z) and the stability of the systemThree. Solving state equation by time domain methodSolution of state equation for 8.5 discrete systemsFirst, the time domain method is used to solve the state equations of discrete systemsTwo. Solving the state equation of discrete system by Z transformThree, the system function matrix H (z) and the stability of the systemControllability and observability of 8.6 systemsFirst, the linear transformation of state vectorTwo, the controllability and observability of the systemExercise 8.32Appendix a convolution integral tableAppendix two convolution and tableAppendix three Fourier coefficients table of commonly used periodic signalsAppendix four Fourier transform tables of commonly used signalsAppendix five Laplasse inverse exchange tableAppendix six sequence of the Z transform table。

信号与系统（Signals and Systems）信号与系统（Signals and Systems）是电子信息工程领域中非常重要的一门课程。

它是研究信号在各种系统中传输、变换和处理的学科，通常需要一些微积分和线性代数的基础知识。

信号和系统理论不仅应用于工程中，也广泛出现在生物医学、电力系统、通信系统中。

总的来说，信号与系统可以分为三个部分：信号、系统和信号处理。

下面我将分别介绍这三个方面的内容。

一、信号信号是代表某种信息的物理量，可以是电信号、光信号、声波等。

常见的信号包括连续信号和离散信号。

连续信号指的是在一段时间内连续地变化的信号，可以用函数f(t) 来表示。

离散信号则是在特定的时间点（离散时间）上产生的信号，表示为序列{xn}。

无论是连续信号还是离散信号，它们都遵循一些基本的信号特性，比如幅度、频率、相位、周期和能量等。

二、系统系统是用于处理信号的工具，可以是电路、滤波器、放大器或者是数字信号处理器。

在信号和系统领域，系统可以被分为连续系统和离散系统。

连续系统指的是输入和输出都是连续信号的系统，比如电路。

离散系统则是输入和输出都是离散信号的系统，比如数字滤波器。

系统通常被描述为输入到输出之间的关系，这个关系可以用一个函数 h(t) 或者 h[n] 来表示。

一个系统可以具有不同的特性，比如时域特性、频域特性、稳定性、因果性、线性性和时变性等。

学习系统理论可以帮助我们更好地了解各种信号和系统的行为特点，从而选择合适的系统来处理不同类型的信号。

三、信号处理信号处理指的是对信号进行分析、处理或者变换的过程，可以是模拟信号处理或数字信号处理。

在信号处理领域，我们经常遇到需要从原始信号中提取特定信息的问题，比如噪声消除、滤波、增强等。

常见的信号处理方法包括傅里叶变换、卷积、差分方程、滤波等。

这些方法可以在时域或者频域中对信号进行变换，得到更有用的信息。

总结信号与系统是一门重要的学科，它主要研究信号在不同系统中传输、变换和处理的过程。

S T R U C T U R E A N DI N T E R P R E T A T I O N O FSignals andSystemsEdward A.LeePravin VaraiyaUNIVERSITY OF CALIFORNIA AT BERKELEYPrefaceT his textbook is about signals and systems,a discipline rooted in the in-tellectual tradition of electrical engineering(EE).This tradition,however,hasevolved in unexpected ways.EE has lost its tight coupling with the“electrical.”Electricity provides the impetus,the potential,but not the body of the subject.How else could microelectromechanical systems(MEMS)become so importantin EE?Is this not mechanical engineering?Or signal processing?Is this not mathe-matics?Or digital networking?Is this not computer science?How is it that controlsystem techniques are profitably applied to aeronautical systems,structural me-chanics,electrical systems,and options pricing?This book approaches signals and systems from a computational point ofview.It is intended for students interested in the modern,highly digital problemsof electrical engineering,computer science,and computer engineering.In par-ticular,the approach is applicable to problems in computer networking,wirelesscommunication systems,embedded control,audio and video signal processing,and,of course,circuits.A more traditional introduction to signals and systems would be biasedtoward the latter application,circuits.It would focus almost exclusively on lineartime-invariant systems,and would develop continuous-time modelsfirst,withdiscrete-time models then treated as an advanced topic.The discipline,after all,grew out of the context of circuit analysis.But it has changed.Even pure EExiiixiv Prefacegraduates are more likely to write software than to push electrons,and yet westill recognize them as electrical engineers.The approach in this book benefits students by showing from the start that the methods of signals and systems are applicable to software systems,andmost interestingly,to systems that mix computers with physical devices such ascircuits,mechanical control systems,and physical media.Such systems havebecome pervasive,and profoundly affect our daily lives.The shift away from circuits implies some changes in the way the method-ology of signals and systems is presented.While it is still true that a voltage thatvaries over time is a signal,so is a packet sequence on a network.This text de-fines signals to cover both.While it is still true that an RLC circuit is a system,so is a computer program for decoding Internet audio.This text defines systemsto cover both.While for some systems the state is still captured adequately byvariables in a differential equation,for many it is now the values in registers andmemory of a computer.This text defines state to cover both.The fundamental limits also change.Although we still face thermal noise and the speed of light,we are likely to encounter other limits—such as complexity,computability,chaos,and,most commonly,limits imposed by other humanconstructions—before we get to these.A voiceband data modem,for example,uses the telephone network,which was designed to carry voice,and offers asimmutable limits such nonphysical constraints as its3kHz bandwidth.This hasno intrinsic origin in the physics of the network;it is put there by engineers.Similarly,computer-based audio systems face latency and jitter imposed by theoperating system.This text focuses on composition of systems so that the limitsimposed by one system on another can be understood.The mathematical basis for the discipline also changes.Although we still use calculus and differential equations,we frequently need discrete math,set theory,and mathematical logic.Whereas the mathematics of calculus and differentialequations evolved to describe the physical world,the world we face as systemdesigners often has nonphysical properties that are not such a good match forthis mathematics.This text bases the entire study on a highly adaptable formalismrooted in elementary set theory.Despite these fundamental changes in the medium with which we operate, the methodology of signals and systems remains robust and powerful.It is themethodology,not the medium,that defines thefield.The book is based on a course at Berkeley taught over the past four years to more than2,000students in electrical engineering and computer sciences.Thatexperience is reflected in certain distinguished features of this book.First,nobackground in electrical engineering or computer science is assumed.Readersshould have some exposure to calculus,elementary set theory,series,first-orderlinear differential equations,trigonometry,and elementary complex numbers.The appendices review set theory and complex numbers,so this background isless essential.Preface xvApproachThis book is about mathematical modeling and analysis of signals and systems,applications of these methods,and the connection between mathematical mod-els and computational realizations.We develop three themes.Thefirst theme isthe use of sets and functions as a universal language to describe diverse sig-nals and systems.Signals—voice,images,bit sequences—are represented asfunctions with an appropriate domain and range.Systems are represented asfunctions whose domain and range are themselves sets of signals.Thus,for exam-ple,a modem is represented as a function that maps bit sequences into voice-likesignals.The second theme is that complex systems are constructed by connectingsimpler subsystems in standard ways—cascade,parallel,and feedback.The con-nections detennine the behavior of the interconnected system from the behav-iors of component subsystems.The connections place consistency requirementson the input and output signals of the systems being connected.Our third theme is to relate the declarative view(mathematical,“what is”)with the imperative view(procedural,“how to”).That is,we associate mathe-matical analysis of systems with realizations of these systems.This is the heartof engineering.When EE was entirely about circuits,this was relatively easy,because it was the physics of the circuits that was being described by the math-ematics.Today we have to somehow associate the mathematical analysis withvery different realizations of the systems,most especially software.We make thisassociation through the study of state machines,and through the considerationof many real-world signals,which,unlike their mathematical abstractions,havelittle discernable declarative structure.Speech signals,for instance,are far moreinteresting than sinusoids,and yet many signals and systems textbooks talk onlyabout sinusoids.ContentWe begin in chapter1by describing signals as functions,focusing on character-izing the domain and the range for familiar signals that humans perceive,suchas sound,images,video,trajectories of vehicles,as well as signals typically usedby machines to store or manipulate information,such as sequences of words orbits.In chapter2,systems are described as functions,but now the domain andthe range are themselves sets of signals.The telephone handset converts voiceinto an analog electrical signal,and the line card in the telephone central officeconverts the latter into a stream of bits.Systems can be connected to form a morecomplex system,and the function describing these more complex systems is acomposition of functions describing the component systems.xvi PrefaceCharacterizing concretely the functions that describe signals and systems is the content of the book.We begin to characterize systems in chapter3usingthe notion of state,the state transition function,and the output function,all inthe context offinite-state machines.In chapter4,state machines are composedin various ways(cascade,parallel,and feedback)to make more interesting sys-tems.Applications to feedback control illustrate the power of the state machinemodel.In chapter5,time-based systems are studied in more depth,first with discrete-time systems(which have simpler mathematics),and then with contin-uous-time systems.We define linear time-invariant(LTI)systems as infinite statemachines with linear state transition and output functions and zero initial state.The input–output behavior of these systems is now fully characterized by theirimpulse response.Chapter6bridges thefinite-state machines of chapters3and4with the time-based systems of chapter5,showing that they can be combined in useful waysto get hybrid systems.This greatly extends the applicability of LTI systems,be-cause,although most systems are not LTI,many have modes of operation thatare approximately LTI.The concept of modal models is illustrated with super-visory control systems.This chapter alone would justify the unified modelingapproach in this text,because it offers a glimpse of a far more powerful concep-tual framework than either state machines or LTI methods can offer alone.Chapter7introduces frequency decomposition of signals;chapter8intro-duces frequency response of LTI systems;and chapter9brings the two togetherby discussingfiltering.The approach is to present frequency domain concepts asa complementary toolset,different from that of state machines,and much morepowerful when applicable.Frequency decomposition of signals is motivatedfirstusing psychoacoustics,and gradually developed until all four Fourier transforms(the Fourier series,the Fourier transform,the discrete-time Fourier transform,and the discrete Fourier transform)have been described.We linger on thefirstof these,the Fourier series,since it is conceptually the easiest,and then morequickly present the others as generalizations of the Fourier series.LTI systemsyield best to frequency-domain analysis because of the property that complexexponentials are eigenfunctions.Consequently,they are fully characterized bytheir frequency response—the main reason that frequency domain methods areimportant in the analysis offilters and feedback control.Chapter10covers classical Fourier transform material such as properties of the four Fourier transforms and transforms of basic signals.Chapter11appliesfrequency domain methods to a study of sampling and aliasing.Chapters12,13,and14extend frequency-domain techniques to include the Z transform and the Laplace transform.Applications in signal processingand feedback control illustrate the concepts and the utility of the techniques.Mathematically,the Z transform and the Laplace transform are introduced asextensions of the discrete-time and continuous-time Fourier transforms to signalsthat are not absolutely summable or integrable.Preface xvii The unified modeling approach in this text is rich enough to describe a widerange of signals and systems,including those based on discrete events and thosebased on signals in time,both continuous and discrete.The complementarytools of state machines and frequency-domain methods permit analysis andimplementation of concrete signals and systems.Hybrid systems and modalmodels offer systematic ways to combine these complementary toolsets.Theframework and the tools of this text provide a foundation on which to buildlater courses on digital systems,embedded software,communications,signalprocessing,hybrid systems,and control.The Web siteThe book has an extensive companion Web site,/lee_varaiya.It includes:The laboratory component.A suite of exercises based on MATLAB andSimulink®∗help reconcile the declarative and imperative points of view.MATLAB is an imperative programming language.Simulink is a block dia-gram language,in which one connects blocks implementing simpler sub-systems to construct more interesting systems.It is much easier to quicklyconstruct interesting signals and systems using the extensive built-in librariesof MATLAB and Simulink than using a conventional programming languagelike C++,Java,or Scheme.These laboratory exercises involve audio,video,and images,which are much more interesting signals than sinusoids.The applets.An extensive set of interactive applets brings out the imperativeview and illustrates concepts of frequency analysis.These include speech,music,and image examples,interactive applets showingfinite Fourier seriesapproximations,and illustrations of complex exponentials and phasors.Instructor and student aids.A large set of Web pages,arranged by topic,can be used by the instructor in class and by students to review the material.These pages integrate many of the applets,and thus offer more interactiveand dynamic presentation material than what is possible with more conven-tional presentation material.At Berkeley,we use them in the classroom,as asupplement to the blackboard.Qualified instructors can download a snap-shot of the Web pages,including the applets,so a network connection is notrequired in the classroom.Additional sidebars.The Web site includes additional topics in sidebarform,beyond those in the text.For example,there is a discussion of imageencoding methods that are commonly used on the Web.Solutions.Solutions to exercises are available from the publisher to quali-fied instructors.∗MATLAB and Simulink are registered trademarks of The MathWorks,Inc.xviii PrefacePedagogical featuresThis book has a number of highlights that make it well suited as a textbook foran introductory course.1.“Probing Further”sidebars briefly introduce the reader to interesting exten-sions of the subject,to applications,and to more advanced material.Theyserve to indicate directions in which the subject can be explored.2.“Basics”sidebars offer readers with less mathematical background somebasic tools and methods.3.Appendix A reviews basic set theory and helps establish the notation usedthroughout the book.4.Appendix B reviews complex variables,making it unnecessary for studentsto have much background in this area.5.Key equations are boxed to emphasize their importance.They can serve asthe places to pause in a quick reading.In the index,the page numbers wherekey terms are defined are shown in bold.6.The exercises at the end of each chapter are annotated with the letters E,T,or C to distinguish those exercises that are mechanical(E for excercise)from those requiring a plan of attack(T for thought)and from those thatgenerally have more than one reasonable answer(C for conceptualization).NotationThe notation in this text is unusual when compared to standard texts on signalsand systems.We explain our reasons for this as follows:Domains and ranges.It is common in signals and systems texts to use theform of the argument of a function to define its domain.For example,x(n)is a discrete-time signal,while x(t)is a continuous-time signal;X(jω)is thecontinuous-time Fourier transform and X(e jω)is the discrete-time Fourier trans-form.This leads to apparent nonsense like x(n)=x(nT)to define sampling,orto confusion like X(jω)=X(e jω)even when jω=e jω.We treat the domain of a function as part of its definition.Thus,a discrete-time,real-valued signal is a function x:Integers→Reals,and its discrete-timeFourier transform is a function x:Reals→Complex.The DTFT itself is a functionwhose domain and range are sets of functions,DTFT:[Integers→Reals]→[Reals→Complex].Then we can unambiguously write X=DTFT(x).Functions as values.Most texts call the expression x(t)a function.A betterinterpretation is that x(t)is an element in the range of the function x.Thedifficulty with the former interpretation becomes obvious when talking aboutsystems.Many texts pay lip service to the notion that a system is a function byPreface xix introducing a notation like y(t)=T(x(t)).This makes it seem that T acts on thevalue x(t)rather than on the entire function x.Our notation includes set of functions,allowing systems to be defined asfunctions with such sets as the domain and range.Continuous-time convolution,for example,becomesConvolution:[Reals→Reals]×[Reals→Reals]→[Reals→Reals].We then introduce the notation∗as a shorthand,y=x∗h=Convolution(x,h),and define the convolution function by∀t∈Reals,y(t)=(x∗h)(t)= ∞−∞X(τ)y(t−τ)dτ.Note the careful parenthesization.The more traditional notation,y(t)=x(t)∗h(t),would seem to imply that y(t−T)=x(t−T)∗h(t−T).But it is not so!A major advantage of our notation is that it easily extends beyond LTI systems to the sorts of systems that inevitably arise in any real world application,such as mixtures of discrete event and continuous-time systems.Names of functions.We use long names for functions and variables when they have a concrete interpretation.Thus,instead of x we might use Sound.This follows a long-standing tradition in software,where readability is considerably improved by long names.By giving us a much richer set of names to use,this helps us avoid some of the preceding pitfalls.For example,to define sampling of an audio signal,we might writeSampledSound=Sampler T(Sound).It also helps bridge the gap between realizations of systems(which are often software)and their mathematical models.How to manage and understand this gap is a major theme of our approach.How to use this bookAt Berkeley,thefirst11chapters of this book are covered in a15-week,one-semester course.Even though it leaves Laplace transforms,Z transforms,and feedback control systems to a follow-up course,it remains a fairly intense ex-perience.Each week consists of three50-minute lectures,a one-hour problem session,and one three-hour laboratory.The lectures and problem sessions arexx Prefaceconducted by a faculty member while the laboratory is led by teaching assis-tants,who are usually graduate students,but are also often talented juniors orseniors.The laboratory component is based on MATLAB and Simulink,and is closely coordinated with the lectures.The text does not offer a tutorial on MATLAB,although the labs include enough material so that,combined with on-line help,they are sufficient.Some examples in the text and some exercises at the ends ofthe chapters depend on MATLAB.At Berkeley,this course is taken by all electrical engineering and computer science students,and is followed by a more traditional signals and systemscourse.That course covers the material in the last three chapters plus applica-tions offrequency-domain methods to collllnunications systems.The follow-upcourse is not taken by most computer science students.In a program that is morepurely electrical and computer engineering than ours,a better approach mightbe to spend two quarters or two semesters on the material in this text,since theunity of notation and approach would be better than having two disjoint courses,the introductory one using a modern approach,and the follow-up course usinga traditional one.AcknowledgmentsMany people have contributed to the content of this book.Dave Messerschmittconceptualized thefirst version of the course on which the book is based,andlater committed considerable departmental resources to the development ofthe course while he was chair of the EECS department at Berkeley.Randy Katz,Richard Newton,and Shankar Sastry continued to invest considerable resourcesin the course when they each took over as chair,and backed our efforts toestablish the course as a cornerstone of our undergraduate curriculum.This tookconsiderable courage,since the conceptual approach of the course was largelyunproven.Tom Henzinger probably had more intellectual influence over the approach than any other individual,and to this day we still argue in the halls about detailsof the approach.The view of state machines,of composition of systems,and ofhybrid systems owe much to Tom.Gerard Berry also contributed a great deal toour way of presenting synchronous composition.We were impressed by the approach of Harold Abelson and and Gerald Jay Sussman,in Structure and Interpretation of Computer Programs(MIT Press,1996),who confronted a similar transition in their discipline.The title of our bookshows their influence.Jim McLellan,Ron Shafer,and Mark Yoder influenced thisbook through their pioneering departure from tradition in signals and systems,DSP First—A Multimedia Approach(Prentice-Hall,1998).Ken Steiglitz greatlyinfluenced the labs with his inspirational book,A DSP Primer:With Applicationsto Digital Audio and Computer Music(Addison-Wesley,1996).A number of people have been involved in the media applications,exam-ples,the laboratory development,and the Web content associated with the book.Preface xxi These include Brian Evans and Ferenc Kovac.We also owe gratitude for thesuperb technical support from Christopher Hylands.Jie Liu contributed stickymasses example to the hybrid systems chapter,and Yuhong Xiong contributedthe technical stock trading example.Other examples and ideas were contributedby Steve Neuendorffer,Cory Sharp,and Tunc Simsek.For each of the past four years,about500students at Berkeley have taken thecourse that provided the impetus for this book.They used successive versionsof the book and the Web content.Their varied response to the course helpedus define the structure of the book and the level of discussion.The courseis taught with the help of undergraduate teaching assistants.Their commentshelped shape the laboratory material.Several colleagues kindly consented to be interviewed:Panos Antsaklis,Uni-versity of Notre Dame;Gerard Berry,Esterel Technologies;P.R.Kumar,Universityof Illinois,Urbana–Champaign;Dawn Tilbury,University of Michigan,Ann Arbor;Jeff Bier,BDTI;and Xavier Rodet,IRCAM,France.We thank them for sharing theexperience that encouraged them toward a career in electrical and computerengineering.Parts of this book were reviewed by more than30faculty members aroundthe country.Their criticisms helped us correct defects and inconsistencies in ear-lier versions.Of course,we alone are responsible for the opinions expressed inthe book,and the errors that remain.We especially thank:Jack Kurzweil,San JoseState University;Lee Swindlehurst,Brigham Young University;Malur K.Sundare-shan,University of Arizona;St´e phane Lafortune,University of Michigan;RonaldE.Nelson,Arkansas Tech University;Ravi Mazumdar,Purdue University;RatneshKumar,University of Kentucky;Rahul Singh,San Diego State University;PaulNeudorfer,Seattle University;R.Mark Nelms,Auburn University;Chen-Ching Liu,University of Washington;John H.Painter,Texas A&M University;T.Kirubarajan,University of Connecticut;James Harris,California Polytechnic State Universityin San Luis Obispo;Frank B.Gross,Florida A&M University;Donald L.Snyder,Washington University in St.Louis;Theodore E.Djaferis,University of Massachu-setts in Amherst;Soura Dasgupta,University of Iowa;Maurice Felix Aburdene,Bucknell University;and Don H.Johnson,Rice University.These reviews were solicited by Heather Shelstad of Brooks/Cole,DenisePenrose of Morgan-Kaufmann,and Susan Hartman and Galia Shokry of Addison-Wesley.We are grateful to these editors for their interest and encouragement.ToSusan Hartman,Galia Shokry and Nancy Lombardi we owe a special thanks;their enthusiasm and managerial skills helped us and others keep the deadlinesin bringing the book to print.It has taken much longer to write this book than we expected when we em-barked on this projectfive years ago.It has been a worthwhile effort nonetheless.Our friendship has deepened,and our mutual respect has grown as we learnedfrom each other.Rhonda Lee Righter and Ruth Varaiya have been remarkablysympathetic and encouraging through the many hours at nights and on week-ends that this project has demanded.To them we owe our immense gratitude.。

Signals&Systems信号与系统SUM:We learned the transform of signals and their application in system analyze,for example in Time domain analysis,the Fourier Transform and Frequency domain analysis,the Laplace Transform and the Complex Domain Analysis,the Z-transform.SUM:我们学习了信号的变换及其在系统分析中的应用，例如时域分析，傅里叶变换和频域分析，拉普拉斯变换和复域分析，z 变换。

1、What is a signal?--signals carry the information we need.In communIcation technology,we call words,images,datas and so on signals.There are continuous signals and discrete signals.什么是信号?——信号携带我们需要的信息。

在通信技术中，我们把文字、图像、数据等称为信号。

有连续信号和离散信号。

Signals are physical quantities that change over time.信号是随时间变化的物理量。

2、A system is any physical set of components that takes a signal and produces a signal.系统是接收信号并产生信号的任何物理组件集。

A system can be classified as linear or nonlinear,time-variant or time-invariant.We focus on LTI system,that is linear time-invariant.系统可分为线性或非线性，时变或时不变。