《信号与系统(第二版)》全册配套课件

《信号与系统(第二版)》全册配套课件2Signals&Systems3课程说明教学计划学时:80学分:5教学内容课堂理论教学(68学时)课程设计(8学时)课堂习题课(4学时)4课程说明参考书目:《信号与系统分析》

吕幼新张明友电子工业出版社

《信号与系统分析》

闵大镒朱学勇电子科技大学出版社5Chapter1SignalsandSystemsThemathematicaldescriptionandrepresentationsofsignalsandsystems.SignalsandSystemsariseinabroadarrayofapplication.Chapter1SignalsandSystems6Chapter1SignalsandSystems(1)AsimpleRCcircuitSourcevoltageVsandCapacitorvoltageVc(2)Anautomobile7(3)ASpeechSignalChapter1SignalsandSystems8(4)APictureChapter1SignalsandSystems9(5)VerticalWindProfileChapter1SignalsandSystems10信号的描述频率特性通信系统中信息:受信者预先不知道的消息;信号:携带消息的物理量;信号可表示成一个或多个自变量的函数;电压电流系统分析的两个共同的基本点：2.系统：对给定的信号作出响应，并产生新的信号Chapter1SignalsandSystems1.信号（一个或多个自变量）时间特性11§1.1Continuous-TimeandDiscrete-TimeSignals

连续时间信号和离散时间信号§1.1.1ExamplesandMathematicalRepresentationContinuous-TimeSignals ——Theindependentvariableiscontinuous0t0tChapter1SignalsandSystems12Chapter1SignalsandSystems2.Discrete-TimeSignals ——TheindependentvariableisdiscretenisintegernumberContinuous-timesignalsDiscrete-timesignals§1.1.2SignalEnergyandPower v(t)——voltagei(t)——current13Chapter1SignalsandSystemsi(t)+v(t)-RInstantaneouspower

瞬时功率Totalenergy14Chapter1SignalsandSystemsTime-averagedpower平均功率①Energysignal②PowersignalEnergysignal0t0tPowersignal0tNeitherenergy,norpower15Chapter1SignalsandSystems§1.2Transformationsoftheindependentvariable§1.2.1Examplesoftransformationsoftheindependentvariable1.Timeshift(时移)0t1t1Example10otherwisePleaseindicate16Chapter1SignalsandSystems

与波形相同相当于左移（超前）to2.Timereversal(时域反折)0t1t1-t10t1x(-t)isareflectionofx(t)aboutt=0相当于右移（延迟）to173.Time-scaling(尺度变换)Chapter1SignalsandSystems0t1t10t1/2t102t1t1a>1信号压缩a倍0<a<1信号扩展1/a倍①Continuous-timesignals②Discrete-Timesignalsx[an]n,an∈Nx[n]x[2n]x[n/2]-2024n18Chapter1SignalsandSystemsExample1.1Giventhesignalx(t)→x(-3/2t+1)012t1Solution1-101t1Time-shift-101t1Time-reversal-2/302/3t1Time-scalingSolution2-2-10t1Time-reversal-4/3-2/30t1Time-scaling-2/302/3t1Time-shift19§1.2.2PeriodicsignalsChapter1SignalsandSystemsDiscreten,N——integernumberFundamentalPeriod:min(T,N)(T,N)>0Synthesizethesignal'speriodicT1T2当T1/T2为有理数时，为周期的ExampleT=2ContinuousT,N≠0——period其中n1,n2互质其周期20Chapter1SignalsandSystems§1.2.3EvenandOddSignalsEvenOddEvenOddEvenpartofx(t)

偶部Oddpartofx(t)

奇部012t1-2-1012t1/2-2-1012t1/2-1/221Chapter1SignalsandSystems§1.3ExponentialandSinusoidalSignals

复指数信号和正弦信号§1.3.1Continuous-TimeComplexExponentialandSinusoidalSignals1.RealExponentialSignalsaisreala>0a<022Chapter1SignalsandSystemsPeriodicComplexExponentialandSinusoidalSignals①PeriodFundamentalPeriod

基本周期ω0FundamentalFrequency23Chapter1SignalsandSystems②Euler’srelation(尤拉关系)③AveragePower24Chapter1SignalsandSystems④HarmonicrelationBasicSignalCommonPeriodω0FundamentalFrequencykthharmonic25Chapter1SignalsandSystems3.GeneralComplexExponentialSignals26Chapter1SignalsandSystems§1.3.2Discrete-TimeComplexExponentialandSinusoidalSignals

where2.ComplexExponentialSignalsandSinusoidalSignals1.RealExponentialSignalsreal27Chapter1SignalsandSystemsEuler'srelation3.GeneralComplexExponentialSignals28§1.3.3PeriodicityPropertiesofDiscrete-TimeComplexExponentialsChapter1SignalsandSystemsSampling1.2.ω0变化2kπ时信号相同29Chapter1SignalsandSystems(a)ω0=0N=1(b)ω0=π/8N=16(c)ω0=π/4N=8(d)ω0=π/2N=4(e)ω0=πN=2低频高频(f)ω0=3π/2N=4(g)ω0=7π/4N=8(h)ω0=15π/8N=16(i)ω0=2πN=1Figure1.27ω0=2kπ时,信号频率低ω0=(2k+1)π时,信号频率高303.PeriodicityPropertiesChapter1SignalsandSystemsRationalNumberFundamentalPeriodisnotperiodic31ω0不同,信号不同.ω0相差2kπ,信号相同.ω0越大,频率越高.ω0=2kπ时,频率低;ω0=(2k+1)时,频率高.对任意的ω0,信号均为周期的.

为有理数时,

信号为周期的.Chapter1SignalsandSystems324.HarmonicallyrelatedperiodicexponentialsChapter1SignalsandSystemsN1=3N2=8N=n1N1=n2N2=24——FundamentalPeriod=133Chapter1SignalsandSystems§1.4TheUnitImpulseandUnitStepFunctions

单位冲激与单位阶跃函数§1.4.1TheDiscrete-TimeUnitImpulseandUnitStepSequencesUnitImpulsen=00n≠0UnitStepn≥00n<0Samplingproperty

取样特性34Chapter1SignalsandSystems与k无关Siftingproperty

筛选特性①0求和区间对k求和35Chapter1SignalsandSystems求和区间——FirstDifference（一阶差分）BASICSIGNALS时域分析频域分析复频（Z）域分析36Chapter1SignalsandSystems§1.4.2TheContinuous-TimeUnitStepandUnitImpulseFunctions1.UnitStepFunctiont>00t<00t10△t12.UnitImpulseFunction0t>0?t=00t<0AC+-t=037Chapter1SignalsandSystemsUnitImpulseFunction①0t(1)②0t≠00△t0t-△0△t38Chapter1SignalsandSystems②0t≠039Chapter1SignalsandSystems0t≠t00t0t(1)Ifs(t)iseven,and③0τ积分区间or,equivalently0τ积分区间40Chapter1SignalsandSystems§1.4.3ThePropertiesofUnitImpulseFunctions1.SamplingandSiftingproperties①Iff(t)iscontinuousatthepointoft=0②SamplingpropertySiftingproperty41Chapter1SignalsandSystems①设为在t=0连续的任意的普通函数InGeneral0t0t(1)42Chapter1SignalsandSystemsScalingproperty Ifaisreal,a≠0Speciallya=-1——EvenfunctionExample243Chapter1SignalsandSystems§1.4.4信号的计算1.信号的加、减、乘、除Example3442.信号的基本表示Chapter1SignalsandSystems-τ0τt-τ0t0τt01t1101t0t1-101t1-10t101t2012t145Chapter1SignalsandSystems3.信号的微分、积分运算2101234tExample1.7x(t)isdepictedinFigure1.40(a),determinethederivativeofx(t).-1x(t)01234t(2)(-3)(2)46Chapter1SignalsandSystems§1.5Continuous-timeanddiscrete-timesystemsSystemBeconstitutedbysomeunitsContactwithsomeruleThesystem'sfunctionSystemanalysis（系统分析）Systemsynthesizes（系统综合）ResearchsystemContinuous-timesystemDiscrete-timesystem47Chapter1SignalsandSystems§1.5.1SimpleExamplesofSystemsLinearConstant-coefficientDifferentialEquationExample1.9LinearConstant-coefficientDifferentialEquationExample1.848Chapter1SignalsandSystemsContinuous-TimeSystemDiscrete-TimeSystemN-orderLinearConstant-coefficientDifferentialEquationN-orderLinearConstant-coefficientDifferenceEquation49Chapter1SignalsandSystems§1.5.2InterconnectionofSystemsSeriesinterconnection(级联)Parallelinterconnection(并联)Feedbackinterconnection(反馈)System1System2inputoutputSystem1System2inputoutputSystem1System2inputoutput50Chapter1SignalsandSystems§1.6BasicSystemProperties§1.6.1SystemswithandwithoutMemory有记忆、无记忆系统无记忆系统:

在某时刻(t)的输出仅仅与同时刻(t)的输入有关。——memoryless（无记忆）——identitysystem,memoryless①②③summer④delay⑤integrateSystemswithmemory51Chapter1SignalsandSystems§1.6.2InvertibilityandInverseSystems可逆系统与可逆性可逆系统:

不同的输入导致不同的输出（一一对应）。SystemInverseSystem——noninvertiblesystems不可逆系统52Chapter1SignalsandSystems§1.6.3Causality（因果性）因果系统:

在某时刻(t)的输出只取决于同时刻(t)或以前(<t)

的输入。(与该时刻以后的输入无关）③Systemswithoutmemory①②Causalsystems因果系统不可预测系统物理上可实现④53Chapter1SignalsandSystems非因果系统:适用于非时间自变量信号的处理.NotCausal§1.6.4Stability（稳定性）StableSystem①②——notstable——stable54Chapter1SignalsandSystems§1.6.5TimeInvariance（时不变性）时不变系统:系统参数不随时间改变(恒参系统),系统的输出波形仅仅取决于输入波形,而与输入作用的时刻无关.IfTimeinvariant时不变Consideracontinuous-timesystemDelayt0LLDelayt0=timeinvariantsystem≠time-varyingsystem55Chapter1SignalsandSystemsExample1.14Delayt0LLDelayt0EqualTimeinvariantExample1.15NotequalTime-varyingDelayn0LLDelayn056Chapter1SignalsandSystemsExample1.16Delayt0LLDelayt0NotequalTime-varying§1.6.6Linearity（线性）1.InitialState（初始状态）输出取决于输入的全部历史57Chapter1SignalsandSystemsInitialState2.Linearity①Additivity②Scaling——Linear58Chapter1SignalsandSystems3.LinearSystemFullresponse①Zero-inputresponseZero-stateresponseInitialstateInput②Zero-inputlinearityWhen59Chapter1SignalsandSystems③Zero-statelinearityIfExample1.17Example1.18It’salinearsystem.It’sanonlinearsystem.It’sanonlinearsystem.Example1.1960Chapter1SignalsandSystemsExample1.20——nonlinearConsiderIncrementallylinear61Chapter1SignalsandSystems线性系统线性系统的三个特性①微分特性②积分特性频率保持性： 信号通过线性系统不会产生新的频率分量62Chapter1SignalsandSystems作业：61.171.21(d)(e)(f)1.22(d)(g)1.231.24(a)(b)1.26(a)(b)1.271.3163Chapter2LinearTime-invariantSystems64Chapter2LTISystemsConsideralineartime-invariantsystemExample1anLTIsystem02t1012t1L024t1-1024t1L65Chapter2LTISystems§2.1Discrete-timeLTISystems:TheConvolutionSum（卷积和）§2.1.1TheRepresentationofDiscrete-TimeSignalsinTermsofimpulsesSiftingProperty离散时间信号的冲激表示Example2n66Chapter2LTISystems§2.1.2TheDiscrete-TimeUnitImpulseResponsesandtheConvolution-SumRepresentationofLTISystemsTheUnitImpulseResponses单位冲激响应LetLetTime-InvariantUnitImpulseResponses67Chapter2LTISystems2.Convolution-Sum（卷积和）TimeInvariantScalingAdditivityConvolution-Sum（卷积和）系统在n时刻的输出包含所有时刻输入脉冲的影响k时刻的脉冲在n时刻的响应68Chapter2LTISystems3.卷积和的计算①图解法例2.3图解法步骤：㈠反折㈡平移㈢求乘积㈣对每一个n求和循环69Chapter2LTISystemsExample2.4DeterminetheoutputsignalSolution(a)n<0(b)0≤n＜4

70Chapter2LTISystems(d)(c)(e)71Chapter2LTISystemsSummarizing,weobtainLy=11Lx=5Lh=7Ly=Lx+Lh-172Chapter2LTISystems不带进位的普通乘法 适用于因果序列或有限长度序列之间的卷积73Chapter2LTISystemsExample3DetermineSolution3 1 4 2 h[n]2 1 5 x[n]15 5 20 103 1 4 26 2 8 46 5 24 13 22 10y[0]y[1]y[2]y[3]y[4]y[5]y[n]={6,5,24,13, 22,10}n=0,1,2,3,4,574Chapter2LTISystems③多项式算法（适用于有限长度序列）y[n]={6,5,24,13, 22,10}n=0,1,2,3,4,5利用多项式算法求卷积和的逆运算已知y[n]、h[n]→x[n]已知y[n]、x[n]→h[n]75Chapter2LTISystemsExample4Determinex[n]y[n]={6,5,24,13, 22,10}n=0,1,2,3,4,5y(t)076Chapter2LTISystems§2.2Continuous-TimeLTISystems:TheConvolutionIntegral

（卷积积分）§2.2.1TheRepresentationofContinuous-TimeSignalsinTermsofimpulses0△t——SiftingPropertyForexample:77Chapter2LTISystemsAccordingtoSamplingProperty=1§2.2.1TheContinuous-TimeUnitImpulseResponseandthe ConvolutionIntegralRepresentationofLTISystems——TimeInvariant——Scaling78Chapter2LTISystemsConvolutionIntegral卷积积分τ时刻的冲激t时刻的响应§2.3卷积的计算一由定义计算积分例2.6zero-stateoutput79Chapter2LTISystems二图解法例2.7求下列两信号的卷积其余t其余t解：①②③80Chapter2LTISystems④⑤81Chapter2LTISystems§2.3PropertiesofLTISystemsLTI系统的特性可由单位冲激响应完全描述Example2.9①LTIsystem——输入输出关系是唯一的82Chapter2LTISystems②NonlinearSystem非线性系统无法用单位冲激响应完全描述本课程主要研究线性时不变（LTI）系统83Chapter2LTISystems§2.3.1PropertiesofConvolutionIntegralandConvolutionSum1.TheCommutativeProperty(交换律）84Chapter2LTISystems2.TheDistributiveProperty(分配律）85Chapter2LTISystems3.TheAssociativeProperty(结合律）交换积分次序86Chapter2LTISystemsCommutativePropertyAssociativeProperty87Chapter2LTISystems4.含有冲激的卷积①②88Chapter2LTISystems5.卷积的微分、积分性质①微分②积分89Chapter2LTISystems③推广n=1m=-1n>0微分n<0积分90Chapter2LTISystems91Chapter2LTISystemsExampleotherwiseotherwiseSolution10123t0123tIntegral92Chapter2LTISystemsSolution20123t0123t93ExampleConsidertheconvolutionofthetwosignals(1)(1)0t-101t-2-1012t-2-2-1012t-2(-2)94Chapter2LTISystems6几种典型系统①恒等系统②微分器③积分器④延迟器⑤累加器95Chapter2LTISystems§2.3.4LTISystemswithandwithoutMemory1.Discrete-timeSystemItismemorylessAnLTIsystemwithoutmemory2.Continuous-timeSystemAnLTIsystemwithoutmemory96Chapter2LTISystems§2.3.5InvertibilityofLTISystemsLTI系统的可逆性SystemInverseSystemidentitysystem(恒等系统）97Chapter2LTISystems§2.3.6CausalityforLTISystemsLTI系统的因果性1.Discrete-timeSystem与n时刻以后输入有关Causalsystem2.Continuous-timeSystemCausalsystem98Chapter2LTISystemsConsideralinearsystemCausalInitialRest(初始松弛）Foranytimet0§2.3.7StabilityforLTISystems(稳定性）1.Discrete-timeSystem99Chapter2LTISystemsStableSystem2.Continuous-timeSystemabsolutelySummable

绝对可加StableSystem①Thesystemisstable.②absolutelyIntegrable绝对可积Thesystemisnotstable.100Chapter2LTISystems§2.3.8TheUnitStepResponseofanLTISystemsLTI系统的单位阶跃响应Discrete-timeSystemContinuous-timeSystemUnitStepResponseUnitStepResponse101Chapter2LTISystems§2.4SingularityFunctions(奇异函数）§2.4.1TheUnitImpulseasanIdealizedShortPulse0△t02△t102Chapter2LTISystemsExample2.16Example2.17103DefineChapter2LTISystems§2.4.2DefiningtheUnitImpulsethroughConvolution单位冲激的卷积定义Foranyx(t)Foranynormal,whichiscontinuousattimet=0.Lett=0SiftingPropertyTheunitimpulsehasunitarea104Chapter2LTISystems§2.4.3UnitDoubletsandOtherSingularityFunctions单位冲激偶和其它奇异函数DerivativeUnitDoublets1.Ingeneral,ktimes0△t0△t105Chapter2LTISystemsDiscrete-timeSystemContinuous-timeSystemCausalsystemCausalsystemStableSystemStableSystem106Chapter2LTISystems3.PropertiesofUnitDoublets（冲激偶的性质）2.DefiningForany①②107Chapter2LTISystemsIngeneral,③Derivativesofdifferentordersoftheunitimpulse

单位冲激的各阶积分108Chapter2LTISystems§2.5CausalLTISystemsdescribedbyDifferential andDifferenceEquations

用微分方程和差分方程描述的因果LTI系统§2.5.1LinearConstant-coefficientDifferentialEquations

线性常系数微分方程一经典解法1.Homogeneoussolution齐次解特征方程109Chapter2LTISystems①特征方程有N个不同的单根②特征方程有1个r阶重根，其余N-r个根各不相同HomogeneousSolution——NaturalResponse

齐次解自然响应2.ParticularSolution——ForcedResponse

特解受迫响应的函数形式取决于输入的函数形式110Chapter2LTISystems输入特解C（常数）B（常数）

α不是特征单根α是特征单根或111Chapter2LTISystemsExample2.14齐次解：特解：全响应：LTI因果系统初始松弛由系统初始条件确定112Chapter2LTISystems②若初始条件不为零，若初始条件不跃变，代入全响应N阶系统，初始松弛：初始松弛条件下：113Chapter2LTISystems二零输入、零状态解法全响应：1.零输入响应：具有齐次解的形式；假定特征方程含有N个不同的单根2.零状态响应：齐次解的另一部分特解齐次解的一部分114Chapter2LTISystems由初始状态唯一决定零输入响应由零初始状态及输入共同决定零状态响应由初始状态及输入决定自然响应函数形式由输入信号决定受迫响应1.零输入零状态解法2.经典解法三两种响应分解形式的关系115Chapter2LTISystemsExample2.14Zero-input responseZero-state response3.Fullresponse116Chapter2LTISystems§2.5.2LinearConstant-coefficientDifferenceEquations

线性常系数差分方程NthorderRecursiveSolution递推算法RecursiveEquation递归方程InputsignalInitialstate117Chapter2LTISystemsParticularlyN=0NonrecursiveEquation非递归方程UnitimpulseresponseFiniteimpulseresponse(FIR)systemExample2.15Initialrest118Chapter2LTISystems119Chapter2LTISystems由初始状态唯一决定零输入响应由零初始状态及输入共同决定零状态响应由初始状态及输入决定自然响应函数形式由输入信号决定受迫响应1.零输入零状态解法2.经典解法两种响应分解形式的关系120Chapter2LTISystems2.差分方程的经典解法FullHomogeneousParticular①HomogeneoussolutionEigenequation特征方程(a)特征方程有N个不同的单根(b)特征方程有1个r阶重根γ1

其余N-r个根各不相同121Chapter2LTISystems②Particularsolution(ForcedResponse)输入特解

α不是特征单根α是特征单根或122Chapter2LTISystems3.零输入、零状态解法FullZero-inputZero-state①零输入响应：具有齐次解的形式；②零状态响应：齐次解的另一部分特解齐次解的一部分假定特征方程含有N个不同的单根123Chapter2LTISystems由初始状态唯一决定零输入响应由零初始状态及输入共同决定零状态响应由初始状态及输入决定自然响应函数形式由输入信号决定受迫响应全响应零输入零状态解法全响应经典解法4.两种响应分解形式的关系124Chapter2LTISystemsExampleConsideranLTIsystem:DeterminethefullresponseSolution1HomogeneousSolutionParticularSolutionFullSolution125Chapter2LTISystemsInitialState:FullSolutionSolution2Zero-inputSolution126Chapter2LTISystemsZero-stateSolut