信号系统期末试卷(一).doc

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1、信号系统期末试卷（一）1.（12point）considerthesystemillustratedinFigure1,where.Supposetheinputdeterminetheoutput.Figure1Solution:2.（10point）ConsiderthesystemillustratedinFigure2,supposeisshowninFigure3.(a)DeterminethemaximumsamplingintervalTsuchthatisrecoverablefrom(b)Ifsecond,sk

2、etchthespectrumof(c)Ifsecond,determineafiltersothatSolution:(a)So,itshallbesatisfiedwith(b)If,then(c)If,then3.（8point）LetdenotestheFouriertransformofthesignaldepictedinFigure4.(a)Find(b)Find(c)FindSolution:(a)isarealandoddsignal.Thisimpliesthatisanimageryandoddsignal

3、.,Also,.(b)(c)4.（6point）Determinethefunction,fortheLaplacetransformanditsassociatedregionsofconvergence:,ROC:Solution:5.（12point）ConsideranLTIsystemwithinputandoutput(a)Findthesystemfunction,indicatetheROCof(b)Determinetheunitimpulseresponse,isthissystemstable?(c)Com

4、putetheoutputofthissystem,iftheinputsignalisSolution:(a),ROC:(b)Stable!(c)6.（12point）TheinputandoutputofastableLTIsystemarerelatedthroughtheblock-diagramrepresentationshowninFigure5.(a)Determinethesystemfunction,indicatetheROCof(b)Determinetheunitimpulseresponseofthi

5、ssystem,isthissystemcausal?(c)Fortheinput,computetheoutput.Solution:(a),ROC:(b),Causal(c)附：梅森公式信号流图的特征行列式，且有表示由源点到输出点之间第条前向通路的标号表示由源点到输出点之间第条前向通路的增益表示对于第条前向通路特征行列式的余因子。它是除去与第条前向通路相接触的环路外，余下的子图特征行列式。