信号与系统(第二版)英文版 (2009 年度畅销榜NO.2742 )

本书是美国麻省理工学院(MIT)的经典教材之一，讨论了信号与系统分析的基本理论、基本分析方法及其应用。全书共分11章，主要讲述了线性系统的基本理论、信号与系统的基本概念、线性时不变系统、连续与离散信号的傅里叶表示、傅里叶变换以及时域和频域系统的分析方法等内容。本书作者使用了大量在滤波、抽样、通信和反馈系统中的实例，并行讨论了连续系统、离散系统、时域系统和频域系统的分析方法，以使读者能透彻地理解各种信号系统的分析方法并比较其异同。\r\n\r\n 本书可作为通信与电子系统类、自动化类以及全部电类专业信号与系统课程的双语教材，也可以供任何从事信息获取、转换、传输及处理工作的其他专业研究生、教师和广大科技工作者参考。\r\n
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1 SIGNALS AND SYSTEMS \r\n\r\n 1.0 Introduction \r\n\r\n 1.1 Continuous-Time and Discrete-Time Signals \r\n\r\n 1.1.1 Examples and Mathematical Representation \r\n\r\n 1.1.2 Signal Energy and Power \r\n\r\n 1.2 Transformations of the Independent Variable \r\n\r\n 1.2.1 Examples of Transformations of the Independent Variable \r\n\r\n 1.2.2 Periodic Signals \r\n\r\n 1.2.3 Even and Odd Signals \r\n\r\n 1.3 Exponential and Sinusoidal Signals \r\n\r\n 1.3.1 Continuous-Time Complex Exponential and Sinusoidal Signals \r\n\r\n 1.3.2 Discrete-Time Complex Exponential and Sinusoidal Signals \r\n\r\n 1.3.3 Periodicity Properties of Discrete-Time Complex Exponentials \r\n\r\n 1.4 The Unit Impulse and Unit Step Functions \r\n\r\n 1.4.1 The Discrete-Time Unit Impulse and Unit Step Sequences \r\n\r\n 1.4.2 The Continuous-Time Unit Step and Unit Impulse Functions \r\n\r\n 1.5 Continuous-Time and Discrete-Time System \r\n\r\n l.5.1 Simple Examples of Systems \r\n\r\n 1.5.2 Interconnections of Systems \r\n\r\n 1.6 Basic System Properties \r\n\r\n 1.6.1 Systems with and without Memory \r\n\r\n 1.6.2 Invertibility and Inverse Systems \r\n\r\n 1.6.3 Causality \r\n\r\n 1.6.4 Stability \r\n\r\n 1.6.5 Time Invariance \r\n\r\n 1.6.6 Linearity \r\n\r\n 1.7 Summary \r\n\r\n Problems \r\n\r\n LINEAR TIME-INVARIANT SYSTEMS \r\n\r\n 2.0 Introduction \r\n\r\n 2.1 Discrete-Time LTI Systems: The Convolution Sum \r\n\r\n 2.1.1 The Representation of Discrete-Time Signals in Terms of Impulses \r\n\r\n 2.1.2 The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems \r\n\r\n 2.2 Continunus-Time LTI Systems: The Convolution Integral \r\n\r\n 2.2.1 The Representation of Continuous-Time Signals in Terms of Impulses \r\n\r\n 2.2.2 The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems \r\n\r\n 2.3 Properties of Linear Time-Invariant Systems \r\n\r\n 2.3.1 The Commutative Property \r\n\r\n 2.3.2 The Distributive Property \r\n\r\n 2.3.3 The Associative Property ' \r\n\r\n 2.3.4 LTI Systems with and without Memory \r\n\r\n 2.3.5 Invenibility of LTI Systems \r\n\r\n 2.3.6 Cansality for LII Systems \r\n\r\n 2.3.7 Stability for LTI Systems \r\n\r\n 2.3.8 The Unit Step Response of an LTI System \r\n\r\n 2.4 Causal LTI Systems Described by Differential and Difference Equations \r\n\r\n 2.4.1 Linear Constant-Coefficient Differential Equations \r\n\r\n 2.4.2 Linear Constant-CoeHicient Difference Equations \r\n\r\n 2.4.3 Block Diagram Representations of First-Order Systems Described by Differential and Difference Equations \r\n\r\n 2.5 Singularity Functions \r\n\r\n 2.5.1 The Unit Impulse as an Idealized Short Pulse \r\n\r\n 2.5.2 Defining the Unit Impulse through Convolution \r\n\r\n 2.5.3 Unit Doublets and Other Singulanty Functions \r\n\r\n 2.6 Summary \r\n\r\n Problems \r\n\r\n 3 FOURIER SERIES REPRESENTATION OF PERIODIC SIGNALS \r\n\r\n 3.0 Introduction \r\n\r\n 3.1 A Historieal Perspective \r\n\r\n 3.2 The Response of LTI Systems to Complex Exponentials \r\n\r\n 3.3 Fourier Series Representation of Continuous-Time Periodic Signals \r\n\r\n 3.3.1 Linear Combinations of Harmonically Related Complex Exponentials \r\n\r\n 3.3.2 Determination of the Fourier Series Representation of a Continuous-Time Periodic Signal \r\n\r\n 3.4 Convergence of the Fourier Series \r\n\r\n 3.5 Properties of Continuous-Time Fourier Series \r\n\r\n 3.5.1 Linearity \r\n\r\n 3.5.2 Time Shifting \r\n\r\n 3.5.3 Time Reversal \r\n\r\n 3.5.4 Time Scaling \r\n\r\n 3.5.5 Multiplication \r\n\r\n 3.5.6 Conjugation and Conjugate Symmetry \r\n\r\n 3.5.7 Parseval's Relation for Continuous-Time Periodic Signals \r\n\r\n 3.5.8 Summary of Propenies of the Continuous-Time Fourier Series \r\n\r\n 3.5.9 Examples \r\n\r\n 3.6 Fourier Series Representation of Discrete-Time Periodic Signals \r\n\r\n 3.6.1 Linear Combinations of Harmonically Related Complex Exponentials \r\n\r\n 3.6.2 Determination of the Fourier Series Representation of a Periodic Signal \r\n\r\n 3.7 Propedies of Discrete-Time Fourier Series \r\n\r\n 3.7.1 Multiplication \r\n\r\n 3.7.2 First Difference \r\n\r\n 3.7.3 Parseval's Relation for Discrete-Time Periodic Signals \r\n\r\n 3.7.4 Examples \r\n\r\n 3.8 Fourier Series and LTI Systems \r\n\r\n 3.9 Filtering \r\n\r\n 3.9.1 Frequency-Shaping Filters \r\n\r\n 3.9.2 Frequency-Selective Filters \r\n\r\n 3.10 Examples of Continuous-Time Filters Described by Differential Equations \r\n\r\n 3.10.1 A Simple RC Lowpass Filter \r\n\r\n 3.10.2 A Simple RC Highpass Filter \r\n\r\n 3.11 Examples of Discrete-Time Filters Described by Difference Equations \r\n\r\n 3.11.1 First-Order Recursive Discrete-Time Filters \r\n\r\n 3.11.2 Nonrecursive Discrete-Time Filters \r\n\r\n 3.12 Summary \r\n\r\n Problems \r\n\r\n 4 THE CONTINUOUS-TIME FOURIER TRANSFORM \r\n\r\n 4.0 Introduction \r\n\r\n 4.1 Representation of Aperiodic Signals: The Continuous-Time Fourier Transform \r\n\r\n 4.1.1 Development of the Fourier Transform Representation of an Aperiodic Signal \r\n\r\n 4.1.2 Convergence of Fourier Transforms \r\n\r\n 4.1.3 Examples of Continuous-Time Fourier Transforms \r\n\r\n 4.2 The Fourier Tkansform for Periodic Signals \r\n\r\n 4.3 Properties of the Continuous-Time Fourier Transform \r\n\r\n 4.3.1 Linearity \r\n\r\n 4.3.2 Time Shifting \r\n\r\n 4.3.3 Conjugation and Conjugate Symmetry \r\n\r\n 4.3.4 Differentiation and Integration \r\n\r\n 4.3.5 Time and Frequency Scaling \r\n\r\n 4.3.6 Duality \r\n\r\n 4.3.7 Parseval's Relation \r\n\r\n 4.4 The Convolution Property \r\n\r\n 4.4.1 Examples \r\n\r\n 4.5 Ihe Multiplication Property \r\n\r\n 4.5.1 Frequency-Selective Filtering with Variable Center Frequency \r\n\r\n 4.6 Tables of Fourier Properties and of Basic Fourier Transform Pairs \r\n\r\n 4.7 Systems Characterized by Linear Constant-Coefficient Differential Equations \r\n\r\n 4.8 Summary \r\n\r\n Problems \r\n\r\n 5 THE DISCRETE-TIME FOURIER TRANSFORM \r\n\r\n 5.0 Introduction \r\n\r\n 5.1 Representation of Aperiodic Signals: The Discrete-Time Fourier Transform \r\n\r\n 5.1.1 Development of the Discrete-Time Fourier Transform \r\n\r\n 5.1.2 Examples of Discrete-Time Fourier Transforms \r\n\r\n 5.1.3 Convergence Issues Associated with the Discrete-Time Fourier Transform \r\n\r\n 5.2 The Fourier Transform for Periodic Signals \r\n\r\n 5.3 Properties of the Discrete-Time Fourier Transform \r\n\r\n 5.3.1 Periodicity of the Discrete-Time Fourier Transform \r\n\r\n 5.3.2 Linearity of the Fourier Transform \r\n\r\n 5.3.3 Time Shifting and Frequency Shifting \r\n\r\n 5.3.4 Conjugation and Conjugate Symmetry \r\n\r\n 5.3.5 Differencing and Accumulation \r\n\r\n 5.3.6 Time Reversal \r\n\r\n 5.3.7 Time Expansion \r\n\r\n 5.3.8 Differentiation in Frequency \r\n\r\n 5.3.9 Parseval's Relation \r\n\r\n 5.4 The Convolution Property \r\n\r\n 5.4.1 Examples \r\n\r\n 5.5 The Multiplication Property \r\n\r\n 5.6 Tables of Fourier Iransform Properties and Basic Fourier Transform Pairs \r\n\r\n 5.7 Duality \r\n\r\n 5.7.1 Duality in the Discrete-Time Fourier Series \r\n\r\n 5.7.2 Duality between the Discrete-Time Fourier Transform and the Continuous-Time Fourier Series \r\n\r\n S.8 Systems Characterized by Linear Constant-Coefficient Difference Equations \r\n\r\n 5.9 Summary \r\n\r\n Problems \r\n\r\n 6 TIME AND FREQUENCY C OF SIGNALS AND SYSTEMS \r\n\r\n 6.0 Introduction \r\n\r\n 6.1 The Magnitude-phase Representation of the Fourier Transform \r\n\r\n 6.2 The Magnitude-Phase Representation of the Frequency R of LTI Systems \r\n\r\n 6.2.1 Linear and Nonlinear Phase \r\n\r\n 6.2.2 Group Delay \r\n\r\n 6.2.3 Log-Magnitude and Bode Plots \r\n\r\n 6. 3 Time-Domain Properties of Ideal Frequency-Selective Filters \r\n\r\n 6.4 Time-Domain and Frequency-Domain Aspects of Nonideal Filters \r\n\r\n 6. 5 First-Order and Second-Order Continuous-Time Systems \r\n\r\n 6.5.1 First-Order Continuous-Time Systems \r\n\r\n 6.5.2 Second-Order Continuous-Time Systems \r\n\r\n 6.5.3 Bode Plots for Rational Frequency Responses \r\n\r\n 6.6 First-Order and Second-Order Discrete-Time Systems \r\n\r\n 6.6.1 First-Order Discrete-Time Systems \r\n\r\n 6.6.2 Second-Order Discrete-Time Systems \r\n\r\n 6.1 Examples of Time-and Frequency-Domain Analysis of Systems \r\n\r\n 6.7.1 Analysis of an Automobile Suspension System \r\n\r\n 6.7.2 Examples of Discrete-Time Nonrecursive Filters \r\n\r\n 6.8 Summary \r\n\r\n Problems \r\n\r\n 7 SAMPLING \r\n\r\n 7.0 Introduction \r\n\r\n 7.1 Representation of a Continuous-Time Signal by Its Samples: The Sampling Theorem \r\n\r\n 7. 1.1 Impulse-Train Sampling \r\n\r\n 7. 1.2 Sampling with a \r\n\r\n 7.2 Reconstruction of a Signal from Its Samplee Using Interpolation \r\n\r\n 7.3 The Effect of Undersampling: Aliasing \r\n\r\n 7.4 Discrete-Time \r\n\r\n 7.4.1 Digital Differentiator \r\n\r\n 7.4.2 Half-Sample Delay \r\n\r\n 7. 5 Sampling of Discrete-Time Signals \r\n\r\n 7.5.1 Impulse-Train Sampling \r\n\r\n 7.5.2 Discrete-Time Decimation and Interpolation \r\n\r\n 7.6 S \r\n\r\n Problems \r\n\r\n 8 Co \r\n\r\n 8.0 Introduction \r\n\r\n 8.1 Complex \r\n\r\n 8.1.1 Amplitude Modulation with a Complex Exponential Carrier \r\n\r\n 8.1.2 Amplitude Modulation with a Sinusoidal Carrier \r\n\r\n 8.2 Demodulatiou for Sinusoidal AM \r\n\r\n 8.2.1 Synchronous Demodulation \r\n\r\n 8.2.2 Asynchronous Demodulation \r\n\r\n 8.3 Frequency-Division Multiplexing \r\n\r\n 8.4 Single-Sideband Sinusoidal Amplitude Modulation \r\n\r\n 8.5 Amplitude Modulation with a Pulse-Train Carrier \r\n\r\n 8.5.1 Modulation of a Pulse-Train Carrier \r\n\r\n 8.5.2 Time-Division Multiplexing \r\n\r\n 8.6 Pulse-Amplitude Modulation \r\n\r\n 8.6.1 Pulse-Amplitude Modulated Signals \r\n\r\n 8.6.2 Intersymbol Interference in PAM Systems \r\n\r\n 8.6.3 Digital Pulse-Amplitude and Pulse-Code Modulation \r\n\r\n 8.7 Sinusoidal Frequency Modulation \r\n\r\n 8.7.1 Narrowband Frequency Modulation \r\n\r\n 8.7.2 Wideband Frequency Modulation \r\n\r\n 8.7.3 Periodic Square-Wave Modulating Signal \r\n\r\n 8.8 Discrete-Time Medulation \r\n\r\n 8.8.1 Discrete-Time Sinusoidal Amplitude Modulation \r\n\r\n 8.8.2 Discrete-Time Transmodulation \r\n\r\n 8.9 S \r\n\r\n Problems \r\n\r\n 9 THE LAPLACE TRANSFORM \r\n\r\n 9.0 Introduction \r\n\r\n 9.1 The Laplace Transform \r\n\r\n 9.2 The Region of Convergence for Laplace Transforms \r\n\r\n 9.3 The Inverse Laplace Transform \r\n\r\n 9.4 Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot \r\n\r\n 9.4.1 First-Order Systems \r\n\r\n 9.4.2 Second-Order Systems \r\n\r\n 9.4.3 All-Pass Systems \r\n\r\n 9.5 Properties of the Laplace Transform \r\n\r\n 9.5.1 Linearity of the Laplace Transform \r\n\r\n 9.5.2 Time Shifting \r\n\r\n 9.5.3 Shifting in the s-Domain \r\n\r\n 9.5.4 Time Scaling \r\n\r\n 9.5.5 Conjugation \r\n\r\n 9.5.6 Convolution Property \r\n\r\n 9.5.7 Differentiation in the Time Domain \r\n\r\n 9.5.8 Differentiation in the s-Domain \r\n\r\n 9.5.9 Integration in the Time Domain \r\n\r\n 9.5.1O The Initial- and Final-Value Theorems \r\n\r\n 9.5.11 Table of Properties \r\n\r\n 9.6 Some Laplace Transform Pairs \r\n\r\n 9.7 Analysis and Characterization of LTI Systems Dsing the Laplace Transform \r\n\r\n 9.7.1 Causality \r\n\r\n 9.7.2 Stability \r\n\r\n 9.7.3 LTI Systems Characterized by Linear Constant-Coefficient Differential Equations \r\n\r\n 9.7.4 Examples Relating System Behavior to the System Function \r\n\r\n 9.7.5 Butterworth Filters \r\n\r\n 9.8 System Function Algebra and Block Representations \r\n\r\n 9.8.1 System Functions for Interconnections of LTI Systems \r\n\r\n 9.8.2 Block Diagram Representations for Causal LTI Systems Described by Differential Equations and Rational System Functions \r\n\r\n 9.9 The Unilateral Laplace Transform \r\n\r\n 9.9.1 Examples of Unilateral Laplace Transforms \r\n\r\n 9.9.2 Properties of the Unilateral Laplace Transform \r\n\r\n 9.9.3 Solving Differential Equations Using the Unilateral Laplace Transform \r\n\r\n 9.10 S \r\n\r\n Problems \r\n\r\n 10 THE Z-TRANSFORM \r\n\r\n 10.0 Introduction \r\n\r\n 10.1 The z-Transform \r\n\r\n 10.2 The Region of Convergence for the z-Transform \r\n\r\n 10.3 The Inverse z-Transform \r\n\r\n 10.4 Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot \r\n\r\n 10.1.1 First-Order Systems \r\n\r\n 10.4.2 Second-Order Systems \r\n\r\n 10.5 Properties of the z-Transform \r\n\r\n 10.5.1 Linearity \r\n\r\n 10.5.2 Time Shifting \r\n\r\n 10.5.3 Scaling in the z-Domain \r\n\r\n 10.5.4 Time Reversal \r\n\r\n 10.5.5 Time Expansion \r\n\r\n 10.5.6 Conjugation \r\n\r\n 10.5.7 The Convolution Property \r\n\r\n 10.5.8 Differentiation in the z-Domain \r\n\r\n 10.5.9 Ihe Initial-Value Theorem \r\n\r\n 10.5.10 S \r\n\r\n 10.6 Some Common z-Transform Pairs \r\n\r\n 10.1 Analysis and Characterization of LTI Systems Using z-Transforms \r\n\r\n 10.7.1 Causality \r\n\r\n 10.7.2 Stability \r\n\r\n 10.7.3 LTI Systems Characterized by Linear Constant-Coefficient Difference Equations \r\n\r\n 10.7.4 Examples Relating System Behavior to the System Function \r\n\r\n 10.8 System Function Algebra and Block Diagram Representations \r\n\r\n 10.8.1 System Functions for Interconnections of LTI Systems \r\n\r\n 10.8.2 Block Diagram Representations for Causal LTI Systems Described by Difference Equations and Rational System Functions \r\n\r\n 10.9 The Unilateral z-Transform \r\n\r\n 10.9.1 Examples of Unilateral z-Transforms and Inverse Transforms \r\n\r\n 10.9.2 Properties of the Unilateral z-Transform \r\n\r\n 10.9.3 Solving Difference Equations Using the Unilateral z-Transform \r\n\r\n 10.10 S \r\n\r\n Problems \r\n\r\n 11 LINEAR FEEDBACK SYSTEMS \r\n\r\n 11.0 Introduction \r\n\r\n 11.1 Linear Feedback Systems \r\n\r\n 11.2 Some Applications and Consequences of Feedback \r\n\r\n 11.2.1 Inverse System Design \r\n\r\n 11.2.2 Compensation for Nonideal Elements \r\n\r\n 11.2.3 Stabilization of Unstable Systems \r\n\r\n 11.2.4 Sampled-Data Feedback Systems \r\n\r\n 11.2.5 Tracking System \r\n\r\n 11.2.6 Destabilization Caused by Feedback \r\n\r\n 11.3 Root-Loeus Analysls of Linear Feedbaek Systems \r\n\r\n 11.3.1 An Introductory Example \r\n\r\n 11.3.2 Equation for the Closed-Loop Poles \r\n\r\n 11.3.3 The End Points of the Root Locus: The Closed-Loop Poles for K=O and |K|= + \r\n\r\n 11.3.4 The Angle Criterion \r\n\r\n 11.3.5 Properties of the Root Locus \r\n\r\n 11.4 The Nyquist Stability Criterion \r\n\r\n 11.4.1 The Encirclement Property \r\n\r\n 11.4.2 The Nyquist Criterion for Continuous-Time LTI Feedback Systems \r\n\r\n 11.4.3 The Nyquist Criterion for Discrete-Time LTI Feedback Systems \r\n\r\n 11.5 Gain and Phase \r\n\r\n 11.6 S \r\n\r\n Problems \r\n\r\n APPENDIX PARTIAL-FRACTION EXPANSION \r\n\r\n BIBLIOGRAPHY \r\n\r\n ANSWERS \r\n\r\n INDEX \r\n
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2001年7月间, 电子工业出版社的领导同志邀请各高校十几位通信领域方面的老师, 商量引进国外教材问题. 与会同志对出版社提出的计划十分赞同, 大家认为, 这对我国通信事业. 特别是对高等院校通信学科的教学工作会很有好处.

教材建设是高校教学建设的主要内容之一. 编写. 出版一本好的教材, 意味着开设了一门好的课程, 甚至可能预示着一个崭新学科的诞生. 20世纪40年代MIT林肯实验室出版的一套28本雷达丛书, 对近代电子学科. 特别是对雷达技术的推动作用, 就是一个很好的例子.

我国领导部门对教材建设一直非常重视. 20世纪80年代, 在原教委教材编审委员会的领导下, 汇集了高等院校几百位富有教学经验的专家, 编写. 出版了一大批教材, 很多院校还根据学校的特点和需要, 陆续编写了大量的讲义和参考书. 这些教材对高校的教学工作发挥了极好的作用. 近年来, 随着教学改革不断深入和科学技术的飞速进步, 有的教材内容已比较陈旧. 落后, 难以适应教学的要求, 特别是在电子学和通信技术发展神速. 可以讲是日新月异的今天, 如何适应这种情况, 更是一个必须认真考虑的问题. 解决这个问题, 除了依靠高校的老师和专家撰写新的符合要求的教科书外, 引进和出版一些国外优秀电子与通信教材, 尤其是有选择地引进一批英文原版教材, 是会有好处的.

一年多来, 电子工业出版社为此做了很多工作. 他们成立了一个“国外电子与通信教材系列”项目组, 选派了富有经验的业务骨干负责有关工作, 收集了23余种通信教材和参考书的详细资料, 调来了100余种原版教材样书, 依靠由20余位专家组成的出版委员会, 从中精选了40多种, 内容丰富, 覆盖了电路理论与应用. 信号与系统. 数字信号处理. 微电子. 通信系统. 电磁场与微波等方面, 既可作为通信专业本科生和研究生的教学用书, 也可作为有关专业人员的参考材料. 此外, 这批教材, 有的翻译为中文, 还有部分教材直接影印出版, 以供教师用英语直接授课. 希望这些教材的引进和出版对高校通信教学和教材改革能起一定作用.

在这里, 我还要感谢参加工作的各位教授. 专家. 老师与参加翻译. 编辑和出版的同志们. 各位专家认真负责. 严谨细致. 不辞辛劳. 不怕琐碎和精益求精的态度, 充分体现了中国教育工作者和出版工作者的良好美德.

随着我国经济建设的发展和科学技术的不断进步, 对高校教学工作会不断提出新的要求和希望. 我想, 无论如何, 要做好引进国外教材的工作, 一定要联系我国的实际. 教材和学术专著不同, 既要注意科学性. 学术性, 也要重视可读性, 要深入浅出, 便于读者自学, 引进的教材要适应高校教学改革的需要, 针对目前一些教材内容较为陈旧的问题, 有目的地引进一些先进的和正在发展中的交叉学科的参考书, 要与国内出版的教材相配套, 安排好出版英文原版教材和翻译教材的比例. 我们努力使这套教材能尽量满足上述要求, 希望它们能放在学生们的课桌上, 发挥一定的作用.

最后, 预祝“国外电子与通信教材系列”项目取得成功, 为我国电子与通信教学和通信产业的发展培土施肥. 也恳切希望读者能对这些书籍的不足之处. 特别是翻译中存在的问题, 提出意见和建议, 以便再版时更正.



中国工程院院士. 清华大学教授

“国外电子与通信教材系列”出版委员会主任

The concepts of signals and systems arise in a wide variety of fields, and the ideas and techniques associated with these concepts play an important role in such diverse areas of science and technology as communications, aeronautics and astronautics, circuit design,

acoustics, seismology, biomedical engineering, energy generation and distribution systems, chemical process control, and speech processing. Although the physical nature of the signals and systems that arise in these various disciplines may be drastically different, they an have two very basic features in common. The signals, which are functions of one or more independent variables, contain information about the behavior or nature of some phenomenon, whereas the systems respond to particular signals by producing other signals or some desired behavior. Voltages and cunenyd as a function of time in an electrical circuit are examples of signals, and a circuit is itself an example of a system, which in this case responds to applied voltages and currents. As another example, when an automobile driver depresses the accelerator pedal, the automobile responds by increasing the speed of the vehicle. In this case, the system is the automobile, the pressure on the accelerator pedal the input to the system, and the automobile speed the response. A computer program for the automated diagnosis of electrocardiograms can be viewed as a system which has as its input a digitized electrocardiogram and which produces estimates of parameters such as heart rate as outputs. A camera is a system that receives light from different sources and reflected from objects and produces a photograph. A robot arm is a system whose movements are the response to control inputs.

In the many contexts in which signals and systems arise, there are a variety of problems and questions that are of importance. In some cases, we are presented with a specific system and are interested in characterizing it in detail to understand how it will respond to various inputs. Examples include the analysis of a circuit in order to quantify its response to different voltage and current sources and the determination of an aircraft's response characteristics both to pilot commands and to wind gusts.

In other problems of signal and system analysis, rather than analyzing existing systems, our interest may be focused on designing systems to process signals in particular ways. One very common context in which such problems arise is in the design of systems to enhance or restore signals that have been degraded in some way. For example, when a pilot is communicating with an air traffic control tower, the communication can be degraded by the high level of background noise in the cockpit. In this and many similar cases, it is possible to design systems that will retain the desired signal, in this case the pilot's voice, and reject (at least approximately) the unwanted signal, i.e., the noise. A similar set of objectives can also be found in the general area of image restoration and image enhancement. For example, images from deep space probes or earth-observing satellites typically represent degraded versions of the scenes being imaged because of limitations of the imaging equipment, atmospheric effects, and errors in signal transmission in returning the images to earth. Consequently, images returned from space are routinely processed by systems to compensate for some of these degradations. In addition, such images are usually processed to enhance certain features, such as lines (corresponding, for example, to river beds or faults) or tegional boundaries in which there are sharp contrasts in color or darkness .

In addition to enhancement and restoration, in many applications there is a need to design systems to extract specific pieces of information from signals. The estimation of heart rate from an electrocardiogram is one example. Another arises in economic forecasting. We may, for example, wish to analyze dte history of an economic time series, such as a set of stock market averages, in older to estimate trends and other characteristics such as seasonal variations that may be of use in making predictions about future behavior. In other applications, the focus may be on the design of sigltals with particular propenies.

Specifically, in communications applications considerable attention is paid to designing

signals to meet the constraints and requirements for successful transmission. For exam- ple, long distance communication through the atmosphere requires the use of signals with frequencies in a particular part of the electromagnetic spectrum. The design of communication signals must also take into account the need for reliable reception in the presence of both distortion due to transmission through the atmosphere and interference from other signals being transmitted simultaneously by other users.

Another very important class of applications in which the concepts and techniques of signal and system analysis arise are those in which we wish to modify or control the characteristics of a given system, perhaps through the choice of specific input signals or by combining the system with other systems. Illustrative of this kind of application is the design of control systems to regulate chemical processing plants. Plants of this type are equipped with a variety of sensors that measure physical signals such as temperature, humidity, and chemical composition. The control system in such a plant responds to these sensor signals by adjusting quantities such as flow rates and temperature in order to regulate the ongoing chemical process. The design of aircraft autopilots and computer control systems represents another example. In this case, signals measuring aircraft speed, altitude, and heading are used by the aircraft's control system in order to adjust variables such as throttle setting and the position of the rudder and ailerons. These adjustments are made to ensure that the aircraft follows a specified course, to smooth out the aircraft's ride, and to enhance its responsiveness to pilot commands. In both this case and in the previous example of chemical process control, an important concept, referred to as feedback, plays a major role, as measured signals are fed back and used to adjust the response characteristics of a system.

The examples in the wide variety of applications for the concepts of signals and systems. The importance of these concepts stems not only from the diversity of phenomena and processes in which they arise, but also from the collection of ideas, analytical techniques, and methodologies

that have been and are being developed and used to solve problems involving signals and systems. The history of this development extends back over many centuries, and although most of this work was motivated by specific applications, many of these ideas have proven to be of central importance to problems in a far larger variety of contexts than those for which they were originally intended. For example, the tools of Fourier analysis, which form the basis for the frequency-domain analysis of signals and systems, and which we will develop in some detail in this book, can be traced from problems of astronomy studied by the ancient Babylonians to the development of mathematical physics in the eighteenth and nineteenth centuries.

In some of the examples that we have mentioned, the signals vary continuously in time, whereas in others, their evolution is described only at discrete points in time. For example, in the analysis of electrical circuits and mechanical systems we are concerned with signals that vary continuously. On the other hand, the daily closing stock market average is by its very nature a signal that evolves at discrete points in time (i.e., at the close of each day). Rather than a curve as a function of a continuous variable, then, the closing stock market average is a sequence of numbers associated with the discrete time instants at which it is specified. This distinction in the basic description of the evolution of signals and of the systems that respond to or process these signals leads naturally to two parallel framework for signal and system analysis, one for phenomena and processes that are described in continuous time and one for those that are described in discrete time.

The concepts and techniques associated both with continuous-time signals and systems and with discrete-time signals and systems have a rich history and are conceptually closely related. Historically, however, because their applications have in the past been sufficienay different, they have for the most part been studied and developed somewhat separately. Continuous-time signals and systems have very strong roots in problems associated with physics and, in the more recent past, with electrical circuits and communications.

The techniques of discrete-time signals and systems have strong roots in numerical analysis, statistics, and time-series analysis associated with such applications as the analysis of economic and demographic data. Over the past several decades, however, the disciplines of continuous-time and discrete-time signals and systems have become increasingly entwined and the applications have become highly interrelated. The major impetus for this has come from the dramatic advances in technology for the implementation of systems and for the generation of signals. Specifically, the continuing development of high-speed digital computers, integrated circuits, and sophisticated high-density device fabrication techniques has made it increasingly advantageous to consider processing continuous-time signals by representing them by time samples (i.e., by converting them to discrete-time signals). As one example, the computer control system for a modern high-performance aircraft digitizes sensor outputs such as vehicle speed in order to produce a sequence of sampled measurements which are then processed by the control system.

Because of the growing interrelationship between continuous-time signals and systems and discrete-time signals and systems and because of the close relationship among the concepts and techniques associated with each. we have chosen in this text to develop the concepts of continuous-time and discrete-time signals and systems in parallel. Since many of the concepts are similar (but not identical), by treating them in parallel, insight and intuition can be shared and both the similarities and differences between them become better focused. In addition, as will be evident as we proceed through the material, there are some concepts that are inherently easier to understand in one framework than the other and. once understood, the insight is easily transferable. Furthermore, this parallel treatment greatly facilitates our understanding of the very important practical context in which continuous and discrete time are brought together, namely the sampling of continuous-time signals and the processing of continuous-time signals using discrete-time systems.

As we have so far described alem, the notions of signals and systems are extremely general concepts. At this level of generality, however, only the most sweeping statements can be made about the nature of signals and systems, and their properties can be discussed only in the most elementary terms. On the other hand, an important and fundamental notion in dealing with signals and systems is that by carefully choosing subclasses of each with particular properties that can then be exploited, we can analyze and characterize these signals and systems in great depth. The principal focus in this book is on the particular class of linear time-invariant systems. The properties of linearity and time invariance that define this class lead to a remarkable set of concepts and techniques which are not only of major practical importance but also analytically tractable and intellectually satisfying.

As we have emphasized in this foreword, signal and system analysis has a long history out of which have emerged some basic techniques and fundamental principles which have extremely broad areas of application. Indeed, signal and system analysis is constantly evolving and developing in response to new problems, techniques, and opportunities. We rully expect this development to accelerate in pace as improved technology makes possible the implementation of increasingly complex systems and signal processing techniques.

In the future we will see signals and systems tools and concepts applied to an expanding scope of applications. For these reasons, we feel that the topic of signal and system analysis represents a body of knowledge that is of essential concern to the scientist and engineer.

We have chosen the set of topics presented in this book, the organization of the presentation, and the problems in each chapter in a way that we feel will most help the reader to obtain a solid foundation in the fundamentals of signal and system analysis; to gain an understanding of some of the very important and basic applications of these fundamentals to problems in filtering, sampling, communications, and feedback system analysis: and to develop some appreciation for an extremely powerful and broadly applicable approach to formulating and solying complex problems.