西安交通大学信号与系统chapter2(2015)

西安交通大学《信号与系统B》课程教学大纲（说明：信通系应该学的是《信号与系统A》，但是找不到A的大纲。

只找到了西交大电子、计算机等专业的《信号与系统B》的大纲，因为用的教材是一样的，大家就凑活着用吧）英文名称：Signals and Systems B课程编号：INFT3014学时：68 （讲课60 ，实验8 ）；学分：4.0 开课时间：秋季学期适用对象：电子科学与技术、计算机科学与技术专业、光信息科学与技术专业先修课程：数学分析（工程类）或高等数学、电路使用教材及参考书：1. 阎鸿森、王新凤、田惠生编《信号与线性系统》，西安交通大学出版社，1999 年8 月第一版2. [ 美] A.V. 奥本海姆等著，刘树棠译，《信号与系统》（第二版），西安交通大学出版社，1998 年一.课程性质、目的和任务“信号与系统”是电气与电子信息类各专业本科生继“电路”或“电路分析基础”课程之后必修的重要主干课程。

该课程主要研究确知信号的特性，线性时不变系统的特性，信号通过线性时不变系统的基本分析方法，信号与系统分析方法在某些重要工程领域的应用，以及数字信号处理的基础知识。

通过本课程的学习，使学生掌握信号分析、线性系统分析及数字信号处理的基本理论与分析方法，并对这些理论与方法在工程中的某些应用有初步了解。

为适应信息科学与技术的飞速发展及在相关专业领域的深入学习打下坚实的基础。

同时，通过习题和实验，学生应在分析问题与解决问题的能力及实践技能方面有所提高。

该课程是学习《现代通信原理》、《自动控制理论》等后续课程所必备的基础。

二.教学基本要求通过本课程的学习，在掌握连续时间信号与系统和离散时间信号与系统分析以及数字信号处理的基本理论和方法方面应达到以下基本要求：1. 掌握信号与系统的基本概念，信号与系统的描述方法，基本信号的特性，系统的一般性质，系统的互联，增量线性系统的等效方法。

2. 掌握信号分解的基本思想及信号在时域、频域和变换域进行分解的基本理论及描述方法。

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。

第一章1.3 解：(a). 2401lim(),04Tt T TE x t dt e dt P ∞-∞∞→∞-====⎰⎰(b) dt t x TP T TT ⎰-∞→∞=2)(21lim121lim ==⎰-∞→dt T TTT∞===⎰⎰∞∞--∞→∞dt t x dt t x E TTT 22)()(lim(c).222lim()cos (),111cos(2)1lim()lim2222TT TTTT T TTE x t dt t dt t P x t dt dt TT∞∞→∞--∞∞→∞→∞--===∞+===⎰⎰⎰⎰(d) 034121lim )21(121lim ][121lim 022=⋅+=+=+=∞→=∞→-=∞→∞∑∑N N n x N P N Nn n N N N n N 34)21()(lim202===∑∑-∞=∞→∞nNNn N n x E (e). 2()1,x n E ∞==∞211lim []lim 112121N NN N n N n NP x n N N ∞→∞→∞=-=-===++∑∑ (f) ∑-=∞→∞=+=NNn N n x N P 21)(121lim 2∑-=∞→∞∞===NNn N n x E 2)(lim1.9. a). 00210,105T ππω===; b) 非周期的； c) 00007,,22mN N ωωππ=== d). 010;N = e). 非周期的； 1.12 解：∑∞=--3)1(k k n δ对于4n ≥时，为1即4≥n 时，x(n)为0，其余n 值时，x(n)为1易有：)3()(+-=n u n x , 01,3;M n =-=- 1.15 解：(a)]3[21]2[][][222-+-==n x n x n y n y , 又2111()()2()4(1)x n y n x n x n ==+-， 1111()2[2]4[3][3]2[4]y n x n x n x n x n ∴=-+-+-+-，1()()x n x n = ()2[2]5[3]2[4]y n x n x n x n =-+-+- 其中][n x 为系统输入。

凯程考研集训营，为学生引路，为学员服务！第 1 页 共 1 页 西安交通大学815信号与系统131分考研经验总结回顾这半年来的艰辛(外校跨考)，从当初的迷茫再到各种找资料，再到每天三点一线的复习，最后也算劳有所获，在这里就专业课的复习有些经验(815信号与系统 131分)，斗胆在这里讲一讲，希望能帮助一些像以前迷茫的我一样的学弟学妹。

1、首先在五六月份我抽空做了做基础的信号与系统，先学好这门课。

当初只是做了一遍 郑君里的信号的课后题，也不多，全部做一遍。

后来买了西交大指定的书籍，有信号与系统三一丛书那本参考书，做了一遍课后题，学过数字信号处理后你会发现信号与系统并不难只是基础而已，交大的考研难度也在数字信号处理上。

还有买了交大指定的数字信号处理邹里和的教材，和配套的二十一世纪丛书的数字信号处理的参考书，那本书很薄。

我建议大家在9月份之前把这三本书的课后题做熟，加上郑君里的就是四本了。

这些都只是基础，一定要扎实，第一遍做有不会的可以标出来，做的时候尽量别看答案。

第二遍再做那些不会的就可以节省时间。

2、9月中旬快十月份的样子，要开始刷题了。

可以找到交大08年之前的十套左右真题，中科大(不是中科院)13年之前的信号真题，上海交大的近年真题。

我当初都打印出来，西交做了三遍左右，剩下两个做了两遍，可以过一段时间拿出来练练，练练做题的感觉。

3、接下来我发现交大的数字信号处理每次都是挺难的，有50分左右，靠第一轮那四本书很难应付，于是我下载了 离散时间信号处理(奥本海姆着)中文版和英文版，记好了这本书是关键!!你可以发现这本书的课后题非常好，分三类，基础题，基本题，和深入题三种。

由易到难。

中文版只是翻译的，课后题的答案只有基础题的，但英文版原着很全面，所有题的答案都有，所以英文版必不可少!时间比较紧，不可能把所有章节题目做完。

我在那段时间将重要的几章比如dft ，dfs ，fft,fir,iir 那几章的英文版课后题答案打印了下来，当初还费了不少劲，找了个pdf 分割器把那几个部分的题和答案整合在了一起，那也打印了一百多页。