信号与系统-双语-奥本海姆-第二章.ppt

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1、Chapter2LinearTime-invariantSystems1Chapter2LTISystemsExample1anLTIsystem02t1012t1L024t1-1024t1L2Chapter2LTISystems§2.1Discrete-timeLTISystems:TheConvolutionSum（卷积和）§2.1.1TheRepresentationofDiscrete-TimeSignalsinTermsofimpulsesExample2n3Chapter2LTISystems§2.1.2TheDis

2、crete-TimeUnitImpulseResponsesandtheConvolution-SumRepresentationofLTISystemsTheUnitImpulseResponses单位冲激响应2.Convolution-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4Chapter2LTISystems3.卷积和的计算①利用定义计算例2.3②图解法Example2.4Determinetheoutputsignal5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6

3、Chapter2LTISystemsExample2.4Determinetheoutputsignal7Chapter2LTISystems③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Example3Determine④多项式算法（适用于有限长度序列）利用多项式算法求卷积和的逆运算8Chapter2LTISystems§2.2Continuous-TimeLTISystems:TheConvolutionIntegral（卷积积分）§2.2.1TheRepresentationofContinuous-Tim

4、eSignalsinTermsofimpulses——SiftingProperty§2.2.2TheContinuous-TimeUnitImpulseResponseandtheConvolutionIntegralRepresentationofLTISystems9Chapter2LTISystems§2.3卷积的计算1.由定义计算卷积积分例2.62.图解法例2.7求下列两信号的卷积其余t其余t3.利用卷积积分的运算性质求解10Chapter2LTISystems§2.3PropertiesofLTISystemsLTI

5、系统的特性可由单位冲激响应完全描述Example2.9①LTIsystem②NonlinearSystem③Time-variantSystem11Chapter2LTISystems§2.3.1PropertiesofConvolutionIntegralandConvolutionSum1.TheCommutativeProperty(交换律）12Chapter2LTISystems2.TheDistributiveProperty(分配律）13Chapter2LTISystems3.TheAssociativeProper

6、ty(结合律）CommutativePropertyAssociativeProperty14Chapter2LTISystems4.含有冲激的卷积①②15Chapter2LTISystems5.卷积的微分、积分性质①微分性质②积分性质③推广形式n>0微分n<0积分16Chapter2LTISystems特殊地n=1m=-1ExampleotherwiseotherwiseConsidertheconvolutionofthetwosignals17ExampleConsidertheconvolutionofthetwosig

7、nalsChapter2LTISystems18Chapter2LTISystems6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19Chapter2LTISystems§2.3.4LTISystemswithandwithoutMemory1.Discrete-timeSystemAnLTIsystemwithoutmemory2.Continuous-timeSystemAnLTIsystemwithoutmemory20Chapter2LTISystems§2.3.5InvertibilityofLTISyste

8、msLTI系统的可逆性SystemInverseSystemidentitysystem(恒等系统）21Chapter2LTISystems§2.3.6CausalityforLTISystemsLTI系统的因果性1.Discrete-timeSystemCau