信号与系统奥本海姆_习题答案

CHAPTER1ANSWERS16ANOBECAUSEWHENT0,01TXBNOBECAUSEONLYIFN0,HASVALUABLE2NCYESBECAUSEKKMNKMX4144KNKK414N419AT/5BECAUSE10,T2/10/50WBNOTPERIODICBECAUSE,WHILEISNOTPERIODIC,ISNOTPERIODICJTETX2T2TXCN2BECAUSE7,N2/M,ANDM70W0DN10BECAUSE,THATIS3/5,N2/M,ANDM3NJJENX5/310/40W0WENOTPERIODICBECAUSE3/5,N2/M10M/3,ITSNOTARATIONALNUMBER0W0114A13,T10,A23,T21OR1SOLUTIONXTISISDTXBECAUSE,3GT3GT1OR3GT3GT1KTTG2DTXDTX115AYN2XN25XN32XN4SOLUTION32122NXXNY11Y432411NXXXX435211NNTHEN,XXYBNOFORITSLINEARITYTHERELATIONSHIPBETWEENANDISTHESAMEINOUTRELATIONSHIPWITHA1NY2XYOUCANHAVEATRY116ANOFOREXAMPLE,WHENN0,Y0X0X2SOTHESYSTEMISMEMORYBYN0WHENTHEINPUTIS,NATHEN,SOYN022YCNOFOREXAMPLE,WHENXN0,YN0WHENXN,YN0NASOTHESYSTEMISNOTINVERTIBLE117ANOFOREXAMPLE,SOITSNOTCAUSAL0XYBYESBECAUSE,SIN1TTSIN2TXTYI12BABYA121SOLUTIONWEHAVEKNOWNABCD122SOLUTIONWEHAVEKNOWNABEG123SOLUTIONFOR21TXTTXEVODTHEN,ABC124SOLUTIONFOR21NXNXEVODTHEN,ABC125APERIODICT/2SOLUTIONT2/4/2BPERIODICT2SOLUTIONT2/2DPERIODICT05SOLUTION4COSTUETXV4COS21TUCSTT4OSO,T2/405126APERIODICN7SOLUTIONN7,M3M7/62BAPERRIODICSOLUTIONN,ITSNOTRATIONALNUMBER18/EPERIODICN16SOLUTIONASFOLLOW62COSSIN4CO2NNXINTHISEQUATION,ITSPERIODISN2M/48,M1S,ITSPERIODISN2M/816,M18IN,ITSPERIODISN2M/24,M162COSSO,THEFUNDAMENTALPERIODOFISN8,16,416NX131SOLUTIONBECAUSE1,2312TXTTTXACCORDINGTOLTIPROPERTY,11312TYTYTYTEXTRAPROBLEMS1SUPPOSESKETCHTDXYSOLUTION2SUPPOSESKETCH1123TTTG2KTT2SOLUTION12CHAPTER221SOLUTIONBECAUSEXN1201,HN202,THEN1ASO,42124121NNNYBACCORDINGTOTHEPROPERTYOFCONVOLUTIOIN12C3NY23SOLUTIONHXKNKKKU2212102NUNNNK1UNTHEFIGUREOFTHEYNIS25SOLUTIONWEHAVEKNOWN,ELSWHRNNX091，ELSWHRNN01，9THEN,UUKKNHNXYKKNUNU101SO,Y4KKUNKU6415,THEN4,1,40KNKANDY14KKUNKU410,THEN14,145KNK527SOLUTION2KYNXGNK（A）,1212KKYXGNGNKB,2XN4KKNCSISNOTLTISYSTEMD,XU0222KKKYXGUGNGN28SOLUTION12TTXTHXTY12THEN,THATIS,OTHERSTTTTY,0120,4,3210SOLUTIONAWEKNOWTHEN,TTHTXXYTTHATIS,SO,OTHERSTTTY,01,1,BFROMTHEFIGUREOF,ONLYIF,WOULDCONTAINMERELYTHEREYTYDISCONTINUITIES211SOLUTIONA533TUETUTHTXYDTDTEUTT3TTTTEU5335,35,31,0195393TEDEETTTTTTTTTTTB5/3TUTTTHDTXTG533UEUETTCITSOBVIOUSTHATDTYTG/212SOLUTIONKTKTKTUETUEY33KT3CONSIDERINGFOR,WECANOBTAIN0T30331EEKUETYTKTKTBECAUSEMUSTBENEGETIVE,FORTT219SOLUTIONAWEHAVEKNOWN112NXWN2YFROM1,211EHFROM2,2THEN,2122121EE2NXYNYNYBUT,1432811OR14BFROMA,WEKNOW24221EHE2412NUNHN220A110COSSCOS0DTTDTTUB0HASVALUEONLYON,BUTTT32IN53T5,00DS0C0641512COS2COSDTTUDU0|SCT|2INT223SOLUTIONKTHTTTHXTYKT227SOLUTION,YATDXTDHATDTHTTYXHATDXTDTXTXTDDA240SOLUTIONA,LET,THEN2TYEXDXTYTHSO,22TTTTHEDEUB21TYTXTUT22TTEDUEUD2214TTTTU221|TTTTTEUE14TT246SOLUTIONBECAUSE121233TUDETUEDTXTT3XTFROMLTIPROPERTY,WEKNOWTHETYTWHEREISTHEIMPULSERESPONSEOFTHESYSTEMTHSO,FOLLOWINGEQUATIONCANBEDERIVED1223TUETEFINALLY,13HT247SOLIUTIONACCORDINGTOTHEPROPERTYOFTHELINEARTIMEINVARIANTSYSTEMA2200TYTHXTHXTYB0TTTT20HXHXTYTC12100000TYTHTXTXXTYDTHECONDITIONISNOTENOUGHE00THTXTHXTYD00TYMTXF0000TYTTHXHHTYEXTRAPROBLEMS1SOLUTEHT,HN1652TXYTDTY2121NNSOLUTION1BECAUSE31232652PPPHSO31TUETTHT012YTT42BECAUSE11222IEIEEHII1SO122NUIIIKIEINHNCHAPTER331SOLUTIONFUNDAMENTALPERIOD8T02/4000000000331133244COS8INJKTJTJTJTJTKJTJTJTJTXAEAEAE32SOLUTIONFOR,10A4/2JE4/2JEA3/2JE3/42JEANNJKNKNX/NJNJNJJEEEE5/845/845/425/420NJJJJJJNJJ5/83/3/2215COS45COSN68I3IN233SOLUTIONFORTHEPERIODOFIS,THEPERIODOFISCOSTT3SINT6TSOTHEPERIODOFIS6,IETX/620W35SIN42CSTTO100T221000055TWJTJTWJTJEETHEN,0AAJ5JA2535SOLUTION1BECAUSE,THENHASTHESAMEPERIODAS,112TXTX2TX1TXTHATIS,T2W21211JKTJKWTKTBXEDXTED11JWTJTT11JKWKJKJKEAEA38SOLUTIONKTJWKTX0WHILEISREALANDODD,THEN,T0AKKA,THEN2T2/0ANDFORKA1SOKTJWKETX0TJWTJEAA0011SIN211TATJTJFOR1221020AADTX/1SIN2TTX313SOLUTIONFUNDAMENTALPERIOD8T0/4KTJWKEATX0TJKKHTY0004,0SINKKHJK0JKWTKYTAHEABECAUSE4800411108TXTDTDTSOYT315SOLUTIONKTJWKEATX0TJKKHTY0DTEJWTTAJKK01FOR,0JWHIF,ITNEEDSKA10KTHATIS2,6/2ANDISINTEGER,SOK8K322SOLUTION02110TDTXTADTETTETETJKJKJKWK1210TJKDJ12112JKETJKTJTJKJEJJKJJJKJKJKSIN2CO21JJJK1CS0334SOLUTION4044021816TJTJTTJTTJTHHEDEDJJAPERIODICCONTINOUSSIGNALHASFOURIERSERIES0JKTKXTAETISTHEFUNDAMENTALPERIODOFXT02/TTHEOUTPUTOFLTISYSTEMWITHINPUTEDIST0JKTKYAHEITSCOEFFICIENTSOFFOURIERSERIES0KBAHJAT1,NXTT021KT01/21JKWTJTKTAEDED（NOTEIF,）NXTTKATSO2282164KBAHJBT2,NNXTT01KAT01/23/21112JKWTJKTJKTKTAXEDEDTEDSO,2416KKBAHJCT1,0201/42SIN1JKTJKTKTKAXEDED28SIN16KBHJK335SOLUTIONT,/70/14TKTJWKEATX0TJKKHTY00KBAJWFOR,OTHERISJH,25101,7KJKOTHERWISTHATIS,ANDISINTEGER,SO00254KK81LET,ITNEEDS,FORYTXKBAK17RK337SOLUTION101223415COS2NJJNJNJJNJJJHEHEEEEAPERIODICSEQUENCEHASFOURIERSERIES2JKNNKXNAENISTHEFUNDAMENTALPERIODOFTHEOUTPUTOFLTISYSTEMWITHINPUTEDISXN2JKJNNKKNYAHEITSCOEFFICIENTSOFFOURIERSERIES2JKBAEAN4,SO4KXNK14K231452COSJKNKK3165COS42KBK340SOLUTIONACCORDINGTOTHEPROPERTYOFFOURIERSERIESA2COSCOS20000TTKATKWAEATJKWTJKKBBECAUSEXTXEV2KVKKAACBECAUSETXTTXRE2KKADKKKTJJWA20EFIRST,THEPERIODOFIS13TX3THEN311220DMEXTDTETTATJKJKKTJKMTJKTJKJKJKEADEX22121343APROOF（I）BECAUSEISODDHARMONIC,WHEREFOREVERYNONXT2/JKTTKXTAE0KAZEROEVENK2/2/TJKTKJTTKJKTKXTAEAEITISNOTICEDTHATKISODDINTEGERSORK0THATMEANS2TXTT（II）BECAUSEOF,WEGETTHECOEFFICIENTSOFFOURIERSERIES2TXTT222/00/2/2/222/00111/11JKTJKTJKTTTTTTKJKTJKTTJKTJKTT