信号与系统习题答案

习题3参考答案3.1①00a2sin4nnan0nb)7cos715cos513cos31(cos4)(tttttf②0nanbnn2)1(1)sin441sin331sin221sin(2)(tttttf3.2①AF02cos)1(2nnAFntjnωnennAtf0212cos)(②AF2021sin)1(21sin)1(nnAnnAFn3.3①)(tf为偶函数、奇谐波函数，0nb，只有0a、2a、4a、…②)(tf为奇函数，只有nb3.5①tωjtωjeetf0022414121)(②)(21)(21)(21)()36()36()44()44(22tjtjtjtjtjtjeejeeeejtf3.6tωjtωjtjωtjωtωjtωjeeeeeetf0000003223212312321)(3.72)10cos(3)302cos(2)204cos()(000ttttf3.8①)2(2222ωjωjeeA②jAeaAaAjaω22③ωA2cos22223.9①33jejω②2)(ωje③)()(00④3)(339jeωj⑤)()1(2322ωjωjeej⑥)31(1222jejjω3.10①)8Sa(2)(2②2202202])[()(jj③ωe④1))(Sa(-1))(Sa(j3.11①)2(21ωjF②ω-jejωF3)(③)2(21ωjFdωdj④)(3-)(jωFjωFdωdj⑤-jωejωF)(⑥ω-jeωjF23)2(21⑦)()(jωFdωdωjωF⑧)32(31ωjF⑨jωeωjFFω-j2)2()()0(⑩)(jωFdωdje-jω3.12①)(2sin40nnn②)(2)1(01nnnn3.13①))(Sa(ccct-tk②)2(sin22ttkc3.14①)(2)(3)(25tuetuettt②t21③)2()2(21tt④)3()3(21tutu⑤)Sa(3t⑥t1⑦)()(5sgn.0)()(5sgn.0)(tuettuettt⑧)sin(j10t⑨)1t(je)1t(1)sin(t⑩)()(2tuetuett3.15)(sin2223.16①65j)j(1j2②)(2)(32tuetuett3.17①)()(42tuetuett②)(91)()(98)(32)(42--tuetuetuetutetyttttf3.18135cos312sin3tt3.19①)cos(t②)sin(3t3.20①)()(2tuetuett②)(tutet③)()(sgn2121tuett④)(21)(21tuetuett3.22①)(sat②)(sat③)(sat3.23①160Ts160fs②100Ts100fs③160Ts160fs④1000Ts1000fs3.24①02②02③0④0⑤0⑥023.2516Ts16fs4Ts4fs习题4参考答案4.1①se1-2s②23)(s1③s3e2e-3s2s-④1s3s2⑤)]sin1scos1(e-[11s1s-2⑥84ss22⑦2526ss13ss43⑧4s2-s2224.2①224)(s4s②3es31-③4)-(s-2e1(s2s）④5s2s22⑤2s2s)1s(s22⑥2225)s4(s3s4s⑦1)(s23-32e14(s29s309s）⑧s50s10s5234.3(a))Tsee-(1Ts1Ts-Ts-2(b))e2e-(1Ts2Ts-s2T2(c))e(14s22s-22(d))see(-1s1s-s24.4(a)s-e11(b))e-(1)es(11s2Ts2T(c))e-1)(1(s1s-2(d))e2e-(1)e-(1Ts2Ts-s2TTs-24.5①)()(3tuetuett②)(5)(2)(2tuetuettt③)()3t(sin)t(u)3(cos322tuetett④)(25)(2)(212tuetuetutt⑤)()3t(sin)t(u)3(cos)(tuttu⑥)(4)(t)t(2u)(tuetuettt⑦)(2)(3)t(2u)(2tuetuettt⑧)()()t(tutuetut⑨)()2t(sin21)t(u)2(cos2)(2tuetetutt⑩)(21)(22tuettutett4.6①)()cos(2tutt②)()33tt21()(2tueeetttt③)1()(tutu④)1()1()()()13()12(32tuetuetuetuetttt⑤)]1()()[sin(tutut⑥)2(3tuet4.7①910ss32s2②56s5ss12s3s2324.8①)()2t(sine27)t(u)2(cos3e)(3t-ttuttu②)3()3)-2(t(sine107)3-t(u))32((cose53)3(533)-(t-3)-t(tuttu4.9①)()e23e-(3e-3t-3t2ttut②)2()e212ee23(e2)-t(42)-3(t-2)-2(t-8tu4.10)()3e3e-(-2te-t-2t2ttu4.11①0t)(1)(tetytx041412t)(3-teeetytttf041)t2343()(3-teetytt②03t)(1)(tetytx0)sin(3252-)cos(3503503t103)(-ttteetyttf0)sin(3252-)cos(3503)3t5053(t103)(-ttteetytt4.12①0t233144291243)(4-54-2teeeetytttt②09495t37)(4-teeetyttt4.13)()sin(-tutetett4.140(A)0.02)(40tetit0(V)2.4)(24.0)(40tettutL4.15023231)(32teetutt4.16)()2(3-tuet4.17)2()2(2)1()1(4)(2)(tuttutttutyf4.183212321213211)(HHHGHHGHHHHHsH4.20(a)214232243213543211)(GGHHHGHHHGHHHHHHsH(b)32ss12s3s221(c)243116871687116547165471683216543211GHHGGHHHHHHHHGHHHHHHHHHHHHHHHHHHHHH(d)121GHL,242GHL,363GHL,47654324GHHHHHHL)()()(143232143423231214321LLLLLLLLLLLLLLLLLLLL876543211HHHHHHHPH1187654321HHHHHHHH(s)H4.21)(-GHHL1321,)(-GHHL2432,)(-GHL353,315323524313231321GGHHHGHGHHGHH1)(1LLLLL1HHHH1P543211H111111P2243132212GHHGHH1)(1LL24313254321GHHGHH1HHHHH(s)H4.28系统稳定4.29①系统不稳定②系统稳定③系统不稳定④系统临界稳定⑤系统不稳定⑥系统不稳定4.30①系统不稳定②系统不稳定③系统不稳定④系统临界稳定4.314k时系统稳定4.32①系统稳定②系统不稳定③系统临界稳定