信号与系统奥本海默原版PPT第二章.ppt

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1、2LinearTime-InvariantSystems2.1Discrete-timeLTIsystem:Theconvolutionsum2.1.1TheRepresentationofDiscrete-timeSignalsinTermsofImpulses2.LinearTime-InvariantSystemsIfx[n]=u[n],then2LinearTime-InvariantSystems2LinearTime-InvariantSystems2.1.2TheDiscrete-

2、timeUnitImpulseResponseandtheConvolutionSumRepresentationofLTISystems(1)UnitImpulse(Sample)ResponseLTIx[n]=[n]y[n]=h[n]UnitImpulseResponse:h[n]2LinearTime-InvariantSystems(2)ConvolutionSumofLTISystemLTIx[n]y[n]=?Solution:Question:[n]h[n][n-k]h

3、[n-k]x[k][n-k]x[k]h[n-k]2LinearTime-InvariantSystems2LinearTime-InvariantSystems2LinearTime-InvariantSystems(ConvolutionSum)Soory[n]=x[n]*h[n](3)CalculationofConvolutionSumTimeInversal:h[k]h[-k]TimeShift:h[-k]h[n-k]Multiplication:x[k]h[n-k]Sum

4、ming:Example2.12.22.32.42.52LinearTime-InvariantSystems2.2Continuous-timeLTIsystem:Theconvolutionintegral2.2.1TheRepresentationofContinuous-timeSignalsinTermsofImpulsesDefineWehavetheexpression:Therefore:2LinearTime-InvariantSystems2LinearTime-Invari

5、antSystemsor2LinearTime-InvariantSystems2.2.2TheContinuous-timeUnitimpulseResponseandtheconvolutionIntegralRepresentationofLTISystems(1)UnitImpulseResponseLTIx(t)=(t)y(t)=h(t)(2)TheConvolutionofLTISystemLTIx(t)y(t)=?2LinearTime-InvariantSystemsA.LTI

6、(t)h(t)x(t)y(t)=?BecauseofSo,wecanget(ConvolutionIntegral)ory(t)=x(t)*h(t)2LinearTime-InvariantSystemsB.ory(t)=x(t)*h(t)LTI(t)h(t)(t)h(t)(ConvolutionIntegral)2LinearTime-InvariantSystems2LinearTime-InvariantSystems(3)ComputationofConvolutionInte

7、gralTimeInversal:h()h(-)TimeShift:h(-)h(t-)Multiplication:x()h(t-)Integrating:Example2.62.82LinearTime-InvariantSystems2.3PropertiesofLinearTimeInvariantSystemConvolutionformula:h(t)x(t)y(t)=x(t)*h(t)h[n]x[n]y[n]=x[n]*h[n]2LinearTime-Invari

8、antSystems2.3.1TheCommutativePropertyDiscretetime:x[n]*h[n]=h[n]*x[n]Continuoustime:x(t)*h(t)=h(t)*x(t)h(t)x(t)y(t)=x(t)*h(t)x(t)h(t)y(t)=h(t)*x(t)2LinearTime-InvariantSystems2.3.2TheDistributivePropertyDiscretetime:x[n]*{h1[n]+h2[n]}=x[n]*h1[n]+x[