英文版《信号与系统》第六七八章习题解答

Homework:

6.56.23Chapter6ProblemSolution816.5Consideracontinuous-timeidealbandbassfilterwhosefrequencyresponseisChapter6ProblemSolutionIfistheimpulseresponseofthisfilter,determinea functionsuchthat(b)Asisincreased,doestheimpulseresponseofthefilter getmoreconcentratedorlessconcentratedabouttheorigin?Solution(b)Itwillgetmoreconcentratedabouttheorigin.(a)2Chapter6ProblemSolution6.23ShowninFigure6.23isforalowpassfilter.Determineandsketchtheimpulseresponseofthefilterforeachofthefollowingphasecharacteristics:(a)(b),whereTisaconstant.3(c)Chapter6ProblemSolution4Chapter6ProblemSolution6.27TheoutputofacausalLTIsystemisrelatedtotheinputbythedifferentialequationDeterminethefrequencyresponseofthesystem, andsketchitsBodeplot.5(b)Specify,asafunctionoffrequency,thegroupdelay associatedwiththissystem.Chapter6ProblemSolutiongroupdelay(c)If,determine,theFouriertransformoftheoutput.(d)Usingthetechniqueofpartial-fractionexpansion,determine theoutputfortheinputinpart(c).6(e)Repeatparts(c)and(d),firstiftheinputhasasitsFouriertransformChapter6ProblemSolution7Chapter7ProblemSolution7.1Areal-valuedsignalisknowntobeuniquelydeterminedbyitssampleswhenthesamplingfrequencyis.Forwhatvaluesofisguaranteedtobezero?8Chapter7ProblemSolution7.2Acontinuous-timesignalisobtainedattheoutputofanideallowpassfilterwithcutofffrequency.Ifimpulse-trainsamplingisperformedon,whichofthefollowingsamplingperiodswouldguaranteethatcanberecoveredfromitssampledversionusinganappropriatelowpassfilter?(a)T=0.5×10-3(b)T=2×10-3(c)T=10-4(a)and(c)Samplinginterval9Chapter7ProblemSolution7.3DeterminetheNyquistratecorrespondingtoeachofthefollowingsignals:10Chapter7ProblemSolution7.6DeterminethemaximumsamplingintervalTsuchthatisrecoverablefromthroughtheuseofanidealLPF.Nyquistratemaximumsamplinginterval11Chapter7ProblemSolution7.9ConsiderthesignalwhichwewishtosamplewithasamplingfrequencyoftoobtainasignalwithFouriertransform.Determinethemaximumvalueofforwhichitisguaranteedthat12Chapter8ProblemSolution8.1DetermineasignalsuchthatSolution13Chapter8ProblemSolution8.3Determine.LPFSolutionBeoutofthepassbandofLPF148.22 InFigure(a),asystemisshownwithinputandoutputTheinputsignalhastheFouriertransformshowninFigure(b)Determineandsketch.

Chapter8ProblemSolutionFigure(a)Figure(b)15-7W-5W-3W03W5W7Wω-5W-3W03W5Wω-8W-6W-2W02W6W8Wω-2W02WωChapter8ProblemSolution16Chapter8ProblemSolutionSolution:8.28SSBsystemusinga90ophase-shiftnetworkrequiredtoretaintheuppersideband.90o

phase-shift17Chapter8ProblemSolutionUpperSideband18ProblemsforFourierAnalysisAperiodofExample1DeterminetheFouriertransformof19Example2Arealcontinuous-timesignalwithFouriertransform,andIfiseven,determine.Ifisodd,determine.ProblemsforFourierAnalysisIfisreal,even20ProblemsforFourierAnalysis2.Ifisreal,odd21ProblemsforFourierAnalysisExample3ConsiderthefollowingLTIsystemswithimpulseresponse:1.2.3.IftheinputisDeterminetheoutput1.Solution:22ProblemsforFourierAnalysis2.3.23ProblemsforFourierAnalysisExample4BandpassSamplingSketch.DeterminethemaximumsamplingperiodT.24(b)If,thereisnooverlap.(a)ProblemsforFourierAnalysis25ProblemsforFourierAnalysisExample5InFigure(a),asystemisshownwithinputsignalandoutputsignal.Ifthefollowinginformationaregiven.1.Determine2.Determinetheimpulseresponseofthewholesystem.Iftheinputsignal, determinetheoutputsignal+-26ProblemsforFourierAnalysis1.Determine27+-ProblemsforFourierAnalysis28ProblemsforFourierAnalysisIftheinputsignal