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1、Chapter2LinearTime-invariantSystems1Chapter2LTISystemsConsideralineartime-invariantsystemExample1anLTIsystem02t1012t1L024t1-1024t1L2Chapter2LTISystems§2.1Discrete-timeLTISystems:TheConvolutionSum（卷积和）§2.1.1TheRepresentationofDiscrete-TimeSignalsinTermso
2、fimpulsesSiftingProperty离散时间信号的冲激表示Example2n3Chapter2LTISystems§2.1.2TheDiscrete-TimeUnitImpulseResponsesandtheConvolution-SumRepresentationofLTISystemsTheUnitImpulseResponses单位冲激响应LetLetTime-InvariantUnitImpulseResponses4Chapter2LTISystems2.Convolution
3、-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5Chapter2LTISystems3.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6Chapter2LTISystemsExample2.4DeterminetheoutputsignalSolution(a)n<0(b)0≤n＜47Chapter2LTISystems(d)(
4、c)(e)8Chapter2LTISystemsSummarizing,weobtainLy=11Lx=5Lh=7Ly=Lx+Lh-19Chapter2LTISystems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10Chapter2LTISystemsExample3DetermineSolution3142h[n]215x[n]1552010314262846524132210y[0]y[1]y[2]y[3]y[4]y[5]y[n]={6,5,24,13,22,10}n=0,1,2,
5、3,4,511Chapter2LTISystems③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]12Chapter2LTISystemsExample4Determinex[n]y[n]={6,5,24,13,22,10}n=0,1,2,3,4,5y(t)013Chapter2LTISystems§2.2Continuous-TimeLTISystem
6、s:TheConvolutionIntegral（卷积积分）§2.2.1TheRepresentationofContinuous-TimeSignalsinTermsofimpulses0△t——SiftingPropertyForexample:14Chapter2LTISystemsAccordingtoSamplingProperty=1§2.2.1TheContinuous-TimeUnitImpulseResponseandtheConvolutionIntegralRepresentat
7、ionofLTISystems——TimeInvariant——Scaling15Chapter2LTISystemsConvolutionIntegral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-stateoutput16Chapter2LTISystems二图解法例2.7求下列两信号的卷积其余t其余t解：①②③17Chapter2LTISystems④⑤18Chapter2LTISystems§2.3PropertiesofLTISystemsLTI系统的
8、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19Chapter2LTISystems②NonlinearSystem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20Chapter2LTISystems§2.3.1PropertiesofConvolutionIntegralandConvolutionSum1.TheCommutativeProperty(交换律）21Chapt
