信号与系统(郑君里)习题答案

---2-1(a)11222012()2()1()()()2()()()()2()()()cccdititutetdtdititutdtditutdtdutititdt+∗+=+=⇒==−b−==+++=+++∫∫2021'2'21'2'11)(01)(1RitvRiMiLidtiCteRiMiLidtiC)()(1)(2)()2()(2)()(33020022203304422tedtdMRtvCtvdtdCRtvdtdCLRtvdtdRLtvdtdML=+++++−⇒(c)dtiCiLtv∫==211'101)(===⇒∫dttvLitvLidtdtvLidtd)(1)(1)(10110'1122011)(122111213tidtdLCiiii+=+=)(0(1]1[][101011022110331tedtdRtvRLvdtdRRLCvdtdRCRCvdtdCCµ=+++++⇒(d)+−=++=∫)()()()()(1)()(11111tetRitvtvdttiCtRiteµRCvdtd1)1(1+−⇒µ)(11teVCR=v)()(10tvtµ=)()(1)1(0'0teRvtvRCvv=+−⇒2-40+12)0(,1)0(0)(2)(2)('22===++++rrtrtrdtdtrdtd0222=++αα+−=11αj−−=12αjtteAeAtr2121)(αα+=⇒2A121=−=Ar)sin3(cos2)(21tteeetttt−=+−=−αα22)0(,1)0(0)()(2)('22===++++rrtrtrdtdtrdtd0122=++αα121−==ααteAtAtr−+=)()(21⇒1A321==Atettr−+=)13()(31)(0,0)0()0(0)()(2)('2233====+++++rrrtrdtdtrdtdtrddt0223=++ααα121−==αα0=α321)()(AeAtAtrt++=−⇒1A1A321=−==Artett−+−=)1(1)(2-51)()(,0_)0(),()(2)(tutertetrtrdtd===+2)()(,0_)0(),(3)(2)(tutertedtdtrtrdtd===+3)()(,1_)0(,1_)0(),()(4)(3)(2'22tuterrtedtdtrtrdtdtrdtd====++12r(0+)3r(0+)r’(0+)(1)(1))(tδ0)r(0)r(0-==+(2))()(d)(3)(2)(ttedttedtdtrtrdtdδ==+Q)(tδ)()()(tubtatrdtd∆+=δ)()(tuatr∆=)(3)(2)()(ttuatubtaδδ=∆+∆+-6b3,a==⇒3)0()r(0=+=∴−+ar(3))()(dtd)()(4)(3)(222ttetedtdtrtrdtdtrdtdδ==++Q)(tδ)()()()('22tuctbtatrdtd∆++=δδ)()()(tubtatrdtd∆+=δ)()(tuatr∆=2)()(4)(3)(3)(2)(2)('ttuatubtatuctbtaδδδδ=∆+∆++∆++43c21b0a−===∴1)0()0(=+=−+arr23)0()0(''=+=−+brr2-7t=01t=0S1S212v0(t)EIS2-7tu−=0)0()0(0−−==vEc)()()()()(00tutvtuIRtvtpCucsc==+)()(1)(00tuItvRtvdtdCs=+)()()()()(111tuRIeRItuBeAtrstRCstRCzi+−=+=−−)()()(112tuEetueAttRCtRCzs−−==r()()()(=+=trtrtrzszitRCEe1−)()1tuRIeRIstRCs+−−2-810t0=t1211i(0-)i’(0-)i(0+)i’(0+)22i(t)+≥0t33∞∞−t0-0+11−=0t0)0(i)i(010)0(l-===−−vuc10)]0()0([1)0(1)0(0)0(1)0(0)0(''=−=====−−+−−+cllueLuLiuLii2+0t==++)()(0)()()(tudtdCtitRitidtdLtucc0)()()(22=++⇒titidtdtidtd)(titjtjeAeA)2321(2)2321(1−−+−+=i10)0(,0)0('==++i)23sin(320)(21tetit−=⇒3∞∞−t)()()()(22tedtdtitidtdtidtd=++⇒e)(1010)(tut+=2-9)(th)(tg1)(2)(3)(tedtdtrtrdtd=+2)()()()()(22tetedtdtrtrdtdtrdtd+=++3)(3)(3)()(2)(22tetedtdtedtdtrtrdtd++=+1e)()(ttδ=h(t))(2)(3)('ttrtrdtdδ=+)()(3tuAetht−=)()()()('tuctbtathdtd∆++=δδ)()()(tubtath∆+=δ)(2)(3)(3)()()(''ttubtatuctbtaδδδδ=∆++∆++18,6,2=−==∴cba)(6e-(t)2h(t)-3ttuδ=∴)()(tute=g(t))(2)(3)(ttrtrdtdδ=+)()(3tuAetgt−=)()()(tubtatgdtd∆+=δ)()(tuatg∆=6,2−==⇒ba)(2)(3tuetgt−=⇒(2))()()()()(22tetedtdtrtrdtdtrdtd+=++)()(tteδ=h(t))()()()()('22ttththdtdthdtdδδ+=++)(][)()2321(2)2321(1tueAeAthtjtj−−+−+=11)(2+++=ppppH23132132313213jpjjjpjj−−−−++−−+=tjtjejejth231231)32121()32121()(−−+−−++=t0≥)()23sin3123(cos)(21tuttetht+=−∫∫∞−==ttdhdhtg0)()()(ττττ)(]1)23sin3123cos([21tuttet++−=−3)(3)(3)()(2)(22tetedtdtedtdtrtrdtd++=+211233)(2+++++++=ppppppH)()()()()()(2'tuetttpHtht−++==δδδ)()2123()()()()()(202tuetdetutdhtgttt−∞−−−+=++==∫∫δτδτττ2-10LTI—∫∞∞−−−=+)()()()(5)(tedtfetrtrdtdτττ)(3)()(ttuetftδ+=−)(th∫∞∞−−−=+)()()()(5)(tedtfetrtrdtdτττe)(3)()(ttuetftδ+=−)()(ttδ=)(2)()()(3)()()()()(5)(ttuetttuetetetftrtrdtdttδδδ+=−+=−∗=+−−)(2)()(5)(ttuetrtrdtdtδ+=+−())()211(2)(11)()5(tpttptrpδδδ++=++=+)5711(41)211(51)(+++=+++=pppppH)()4741()()()(5tueetpHthtt−−+==δ2-12()tue=1)(2)(1tuetrt−=)()(2tteδ=)()(2ttrδ=.(1))(trzi2e)()(3tuett−=)(3tr1)()()(trtrtrzszi+=⇒)()()()()(22)(11trtrtrrtrtrzszitzszi+=+=)()(12trdtdtrzszs=)()()()()()(112121trdtdtrtrtrtrtrzszszszs−=−=−)()(2)()1()()(121ttuetrptrtrtzsδ−=−=−−)(11)()112(11)(1tptpptrzsδδ+=−+−=)()(1tuetrtzs−=())(11)()(1)()(11tppHtpthtetrzsδδ+==∗=1111)(+=÷+=⇒pppppH)()()()(11tuetrtrtrtzszi−=−=2)()(3tuetet−=)()()(111)()()(33tuteetppptepHtrttzs−−−=++==δ)()2()(33tuetrrtrtzszi−−=+=⇒2-13*)(1tf)(2tf)(1tf)(2tf1)()(),()(21tuetftutfat−==2)45cos()(),()(21°+==ttfttfωδ3)2()1()()],1()()[1()(21−−−=−−+=tututftututtf4)1()1()(),cos()(21−−+==tttfttfδδω5)(sin)(),()(21ttutftuetft==−α1ττταταdtuuetuetutftft)()()()()()(21−=∗=∗∫∞∞−−−)1(10ttedeαατατ−−−==∫2)45cos()45cos()()()(21°°+=+∗=∗ttttftfωωδ3−+−+=∗∫∫−2112132,)1(21,)1(3,1,0)()(tttdttdttttftfττττ++−−=32,232121),1(213,1,022ttttttt4)]1(cos[)]1(cos[)]1()1([)cos()()(21−−+=−−+∗=∗ttttttftfωωδδω5ττττττατατdtedtutuetftft)sin()()sin()()()(021−=−−=∗∫∫−∞∞−−)(1cossin2tuettt++−=−ααα2-141)1()()(−−=tututf)(*)()(tftfts=2)2()1()(−−−=tututf)(*)()(tftfts=1)]1()([)]1()([)()()(−−∗−−=∗=tututututftfts)}1()]1()([{)]1()([)(1)(−+−−∗−−=∗=tutututtttfptpfδδ)2()]2()1()[1()1()]1()([−−−−−−−−+−−=tutututtututut)]2()1()[2()]1()([−−−−+−−=tututtututs(t):s(t)1012t2)]2()1([)]2()1([)()()(−−−∗−−−=∗=tututututftfts)}2()]2()1()[1{()]2()1([)(1)(−+−−−−∗−−−=∗=tutututtttfptpfδδ)]4()3()[4()]3()2()[2(−−−−+−−−−=tututtututs(t)2-15)()()(),5()5()(),1()1()(2121321−++=−++=−−+=tttftttftututfδδδδ34s(t)1012t1)(*)()(211tftfts=2)(*)()(212tftfts=)(*2tf3)(*)]}5()5()][(*)({[)(2231tftututftfts−−+=4])(*)()(314tftfts=(1))5()5()()()(11211−++=∗=tftftftfts(2))()]5()5([)()()()(2112211tftftftftftfts∗−++=∗∗=)10()(2)10(111−+++=tftftf(3))(*)]}5()5()][(*)({[)(2231tftututftfts−−+=)()]5()5()][5()5([211tftututftf∗−−+−++=)()]}5()4([)]4()5({[2tftutututu∗−−−++−+=)10()()9()1()1()9()()10(−−−−+++−−+−++=tut