数字信号处理_第四版_sanjit_课后答案[2-7章，英文版]_khdaw

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1、Chapter22.1UsingEq.(2.9),weget:(a)===(b)2.2Toshowthis,westartwiththedefinitionsfromEq.(2.9)andsquarethem:22[]2[]2.21Themiddleinequalityisageneralizationofthetriangleinequality.Wecantakesquarerootsofbothsidesofthisresult,becauseeverythingwithintheequationsisposit

2、ive,getting:2.3(a)[]=[+3]={2016320},60.(b)[]=[2]={8273011},33.(c)[]=[]={0236102},33.(d)[]=[3]+[+3]={825317220},26.(e)[]=[2][]={36},21.(f)[]=[+4][3]={36122483011},55.(g)[]=4.1[]={32.88.228.712.304.14.1},51.2.7(a)Let[]bethesignalinthemiddleofthestructure.Then:Wecanseethat:=++

3、.Puttingthesetogether,weget:[]=0([]1[1]2[2])+1([1]1[2]2[3])+2([2]1[3]2[4])=0[]+(11)[1]+(212)[2](1+2)[3]2[4].(b)Again,ifwelet[]bethesignalinthemiddleofthestructure,then:Notforsale.2=++Wecanseethat:=Combiningtheabovetwoequationsweget:=++(c)Ifwelet[]and[]representthesignals

4、pasteachfeed-forwardcomponent,then:=(++)=++=++Substitutingthetoptwoequationsintothelastequation,weget:=(++)+(++)+(++)=(++)+(++)+(++)+(++)+(++)+(++)+(++)+(++)+(++)whichleadsto:[]=[0][]+[0](11+12+13)[1]+[0](21+1211+22+1113+1213)[2]+[0](1221+1122+1321+111213+1322+1123+1223)[3]+[0

5、](2221+121321+111322+111223+2223)[4]+[0](211322+211223+222311)[5]+[0]212223[6](d)Let0[],1[],anddenotetheoutputsofthethreeadders:=+++=+=+=+Notforsale.3Combiningtheabove,weget=(+)+(+)+(+)+=++++++2.5=Sinceisoflengthanddefinedforthe=convolutionsumreducesto=Thus,willbenonzerofor=al

6、lthosevaluesofandforwhichsatisfiesTheminimumvalueofis0,andoccursforthelowestat=and=Themaximumvalueof=andoccursformaximumvalueofatThus=and=+Hencethetotalnumberofnonzerosamples=+2.6Letbethelengthoftheconvolutionsumof[]and[],whichareoflengthand,respectively.FromProblem2.5,

7、weknowthatThelengthoftheconvolutionof[n]with[],isthus+or++2.7Toshowthatthetwoconvolutionsareequal,wesimplyevaluatebothconvolutionsums:2.8(a)1[]1[]={12321},22.=(b)2[]2[]={121242121},08.=(c)3[]3[]={401201701204},44.=2.9(a)Given[]and[]fromProblem2.3,theirconvolutionsum[

8、]isgivenby:[]=[][]=={16422405279613120},84.(b)Given[]and[