信号与系统题库(完整版)

信号与系统)共)()hht1t)ee)(t)、h、h3t2t5t)(ee)t)3tt232()2t()tete3t、、5352()()tete3t2t55[n]ex50radsCcos20tCcost、C、C、C、C000012Csin20tCsint12Ccos20t1Csin20t1()(Tt))tTkTt)2tf(t)f(t)ft()ft。知f、21T112)4))2)、、、222(k)3(k1)2(k)hkk23(1k)2u(k)kkk(12.72e(t)、、、、t(12.72e(t)t(1e(t)t(e1)(t)t共)1(k)y(k1)y(k2)f(k1)y2h(k)。(t)f(t)f及12（1）f(t)0.5,,1sTsAV1ft)0.5,3,3sTsAV2(t)ft)f与。12f(t)f(t)。12ft)(sint)F(j)。e(sF(s)()ft。s2(t)(t4)u(t)ft)f2dyt)dyt)t)232yt)ft)系统的数学模型为。，则系统的自然频率为2共)[n]cos(n)sin(n)x）42(t)eu(t)h）)tn若fnf((t)(t)h）0若y(n)(n[n()若共)()(t)eU(t2)f(t)e2)U(t2)）f）f）f）f））t(t(t)e2)U(t)ft)tUtt(t)t1)[Ut1)U(tt)tUt1)Utxaxa1fx()求。1dl和0ATT(1)RSf)。()TXX0()5H(s)。HKK0KK(1)(s)F(s)(s)F(s)；;(s2s11tt)tt)．2(t)(t1),h(t)U(t)U(t3)，如图所示零状态系统，h12ft)Ut)Ut1)yt)t(t)y(k3y(k1)2y(k)e(k1)2e(e)y(n)y(n1)ny(0。3(n。1ft)F(s)s22s51f(t)costft()fttft。'()tf0t0S()4e的噪声和希望得到的信号cost()12t)(0)3t,111()14()(0)2tt222drt)t)232rt)r)1,r)22drt)2rt)et),r(0)2,e(t)eUt)tdtttcosft1()22其它0Fj1[()(()22222ttsinft1Fj()()222其它0tt()()f)ft1Fj()3()2230drt)2r(t)e(t),r(0)0,(t)U(t)dtdrdtdt)2rt)3e(t),r(0)0,e(t)U(t)dtddd2t)3rt)2r(t)e(t)e(t),r)1,r)()()eteUt试判断r3t201HR，it)(t)L2(0)V，电感上的初始电流i(0)0ARucLy(k5y(k1)6y(k)e(k)e(k)U(k)(0)2,y(1)1y。zizit)ht)sTt)求（1f(t)tTrt)rT)（r2y(k3y(k1)2y(k)e(k1)2e(k)(k)(2)U(k)y(0)0,y(1)1。ekziziz(2acosza)22H(z)(a1)H(z)在z0z(2acosza)2120~zH(s)s51y(k)y(k1)y(k2)f(k)f(k2)66h(k)。dB，2c120dBdBpsa1)u(n)ejn2y(k)y(k4e(k)2e(k。如图所示，周期矩形信号60MH5kHkHZZZ2ftf())ft()f()(f)f()ftf())(22(k)[(0.5)(0.4)U(k)hkk）sint2cost）ett）2t1xt)Axt)：1etx(0)x(0)xt)1et253ete2txt)1e6et2tt)。(t)eu(t)(a0)f(t)Ecos(t)u(t)）f）at0K(S)F(s)(K0)s2K(s)F(s)(K(ss(s)求H1t)(0)1()yt。x和hx求ftFI()()()2(t)(t1),h(t)(t1),f(t)sintU(t)y(t)h，12f(t)h。3n,0n72,0n5(n)7,n8()xn120,其它0,()()()(),()tAtBetrtCt2210A020,B1,C1001401(s)H；t)a1tataft()a01tft()eUt()aat1ft())ta212a2fte()a2[ftF(s)设已知）1）sint2cost）t2t11[]j，ftFjFj1FjFj)][(Fj1()[()]()[()]求[()]且1001岁求dft)2t)f2z(z)K0HzK(t)sin(t)u(t)f1t)tt)ut)fff2340(t)sin(t)u(tt)0t)tt)utt)00t)ty(t)e，求xtZ(s)K(sz)Z(s)1(sp)(sp)12Cz，p，p112若Z(s)Z(j1C）ut)ut1)utsin[att）0att)0d[esintut)]）tdt11，ut23c）y(n)2y(n1)y(n2)3y(y0。n:n:n2:1:1v(t)0n。123V(s)V(j)(s)H()H、；00E(s)E(j)et)cos(2tV(t)()vt。0(t)ft)f与12[ftE,[ftE,1222111222(t)f(t)f(t)f(t)f1212K(sz)Z(s)Z(s)1(sp)(sp)12,p,pCz112Z(s)Z(j1C(t)()etRt)(t)e；。et)ut)etee）t)0et00t)0(1t)e2tte2tte2t）0(1t)et2。atUt()atbtsin2sina5tb6tc1t257atbsintsin3tcosatbsin3atbt)2(2at2()at3()aetacostbt2sin1eatteat）t)0eatet00t)0t)ete2t）2t0te2t(1t)e2t。H3s2(s)2s3s1a2H(z)T0.5。sintsintsintt),h(t)ht)h。ttt1213s）））s(s2(s4)(s(s4)(s(n)(n)x(n)U(n2)U(n3)2x(n)0.5U(n)xn13(p2)xxft)(1)12x(p2)x012(p2)x(px0(2)12(px(2px012(p3)x6x(p1)ft)(3)12px(p3)x012px(3px0(4)12x(pxft)1212ttt)f120tt)看作是门函数与周期函数cost将f将ft)()2tTutkku(0)0()cc12i)c及t)N)(/)xRx0t)y1x(0)()和x)xk。112R()cosa0x(t)KU。R）et)t)(t)(1eU(t)）e）estE(0t)t)tt)E(0t)E）et)0t,t0)ttU(t)）e）ett)Ut)UtT)]TB(s)s3s2ssK43212t2t(sin)(t)(2e1)U(t)r2tuT(n)()u(n)fn2在下图所示系统中，理想低通滤波器的频率特性H()U2)Ue，2)]ht）()jt00f(t)[Sa(t)]costyt)）f(t)[Sa(t)]sintyt)。220023dB求NH(s);R0.151aldrt)5r(t)e)ft)e(t)f(t)eu(t)3(t)tdtt)h。t)F(s)ftefefefefat。ttt()a()()()ataaa11H(jHj)()22icejt0()Hc0ict)fs2s1ss2s1232）F(s)）F(s)(ss2)(s(ss2)(s2s1s2s3s4s42）F(s)）F(s)s(sss321e2s）F(s)fs(s2t)Sat)ft)f与奈奎斯特周期T。NN16N,FF1215,FF12ffccffccffccy(n)y(nx(n)H(z)h(n)x(n)u(n)kv(t)V(s)(s)H0V(s)1xt)Axt)1e2t(0)()xt当x当x1e2t22e2t(0)()xt1e2teAt和。(n)4DFS[x(n)]X(k)xNppp1()H0E()()rt。2设S()e12s/t)()Fj,)f(t)ft和[99]f202/s(n)nU(n)U(nx(n)x(n)y(n)x(n1)y12(n)x(n1)y(n)x(n1)x(n1)4y35(n)x(n1)x(n1)y(n)x(3n)6yn3n(n)xy(n)x(k)y78kx(n)x(n)x(nx(n)x(n1)x(n)Hzhk。Z(k)k(kfff(k)k(kk(k)(k23z1F(z)25z2z122z））z2）zsintU(t)R0sinatsinttU(t1)））tet）t(k)对于线性非时变系统，已知其对单位函数序列的响应为111[(k)(2)(3)U(k)hh623s(s)(s)(s)y(0)1,y(0)0）H）H）Hs12s2y(0)1,y(0)0s4s4s22y(0)2,y(0)1s2s2t)t)ut)y(t)eu(t)u(1t)ft(t)12eU(t)t)。it求x(t)=t，y(t)=et(t)be、si(t)ut)、it)s(t)5cos1000tcos2000tf2t)为zfU()()HI()R和R12,Ru(t)0(),求R的值,it(无失真12.p423H(p)已知某系统的转移算子，起始条件为p(ppr0,r0rS和S12:(t)(t)Be(t)r(t)C(t)S1111111100,B,C[2,1]A34111S:(t)A()tBet()tr(t)C()2222222222,B1,C1A222()t()t1()t2S和S122k已知离散时间系统的单位函数响应h(k)U(k)，输入信号3e(k)5[U(k)U(k。1e22e2tt2(0)()(0)t)t当11e2tett)。x(n)Anx(n)ej()8n78(t)u3(t)10sintU(tVu。1et)tut)，求t()2z(z)kH（zkk9.5zH(z)(z0.5)(10z)z和z10XtAt()cos(cO至22ARXSf)。()cos()cX2htUt1ht2thtt()()()()(1)()3ht()。(t)u(t)r(t)2eu(t)e(t)(t)et112(2)(t)r。2(t)r；zi(t)eu(t)r(t)3e。t3,)xt)gt)exjt1xt)gt)e,)x2jtV(s)(s)Hs2V(s)1(E)h(n)H。y(n)0.6y(n1)y(nx(n)y(ny(n1)y(n)x(n)y(n)2y(n1)2y(nx(n1)2x(n(s)ht)e(t)H(t)r。)5e9cos[135]R2Xt)UtVx(0)V,x(0)1Af12x(t),x(t)y(t),y(t)）1212(t)x(t)2y(t)1求系统的矩阵指数函数eA(t)x1(2)y2y(n)y(nny(0(1)0n(t)f(t)求f、12atUt)ft)e，f(t)EcostU(t)1203z1x(z)25z2z12z2zz2；；y(k)y(k1)Te(kTe(k)ekaT1t)F(j)()f(0)F()d。设f）Fft）系统的输入输出关系可由二阶常系数线性差分方程描述，如果相对于输入为x(n)u(n)y(n)[235u(n)。nnx(n)2[u(n)u(ny(n)。Y(s)(s)[143](a)HX(s)xt)，求T、T和Tyt().sH(s)H(s)H(s)y(0)1,y'(0)0s12s2y(0)1,y'(0)0s4s4s22y(0)2,y'(0)1s2s2s(1)H(s)(a0)H(z)saah(n)设T2Hs()a(z)H7y(n)bx(nr)rr0(x(n)(n)y(n)y(n)y求g(t)1e2tr(t)1ete2t2te(t)。(s(s））(s2)(s(s(s(n)(n)()y(n)h(n)；x如下，Gn和110()10n()xkk1()H1()20nx(n)a第ny(n)x(n)ay元y(n)n12y,y(k1)0.5y(k)s(k1)2e(k)(0)5()(yekUkzi(t)2cost,tx(t)50cost在图所示系统中，已知f，，m0tH()G)()yt。0m0(z)e(z)()xn。XzV(s)(s)H2V(s)11(n)(n)(n1)某地质勘探测试设备给出的发射信号x，接收回波信号21ny(n)U(n)h(n)y(n)h(nx(n)。2求h(n)；t)byt)cyt)dyt)0系统的微分方程为ay若选取状态变量为x(t)ay(t)，x(t)ayt)by(t)，xt)ayt)byt)cyt)输出取为rt)123yt)A为1002A））A）A02124310At)。t是0与T之间均0S(XYtAXt()(H(s)s3saH()1Ke3a从0tK11H(s)p3zaH()1ke3a从0变到5，kt11M8H(z)h(n)H(z)(s)F。）(ss4)(ss）s(s2)(s22s(k1)x(k)x(k)x112x(k1)x(k)x(k)212y(k)x(k)x(k)e(k)12(0)2,x(0)2x12(k)2U(k)e。kTsin(t)0t)t)2f0为其他值)T）ft)t)2(3pH(p)rr0rp(p4p23p1H(p)rr0,r1p(p2(s)H1102A,B,C11,D1,et)Ut),(0)。1111共)1表试证明题图所示系统可以产生单边带信号。图中信号gt)G()之频谱受限于~;()Hjjsgn().()()()设t之频谱为VVmm0mttcos(nt)n(0,2)(1)e(AB)tee。kHkk01000001Hk00010000ttk121t2!(k1)!tk2e01tHk(k2)!01IHJktt2k1(k1)!1t2!etk2e01tt(k2)!011001000,e求At设A100120002tt)nt)n(0,2)i,t)(j,t)i1)(j1),t]i,t)(j,t)i1)j]t}i,t)sal(j,t)i1)(jtsali,t)cal(j,t)sali1)jr信号与系统答案)共)BA共)2(2)sinkU(k)k410002000kHz,kHz）3331n()ej)S22nU(t1)e2(t2)ut)4(t)，共)共)11CR1t)u()utCRC11(a)b)et)RC10Ct)t)iLi2LLL12ut)ut()2it)1CC()0it)L1it2L11(1)(3)(5)es(2)(4)e2ss1e2s12cos2ssin2ess1s4211112[1(1s)ee(6)eesss2ss2ssss221)G)G)]解AF2A1010j)G)G)]BF2B10201)[F)F)]))]CFCAB00111jj[G()G)G)G22222101202111jG2j[G(G)))G2222110220111jjG(G)))GG)G)]2222211002020g(t)101j)[F)F)]))G)]DF2DAB0020g(t)202sinEs(a)b)[eeee](t)sts(t)sts1122E3[1eTeTe4e]4SS424s1(c)(1e)e0ts21e2s2E11(d)[1eee]ts(Tt)s00ts1e20SfXRed()jtAT2AT()22()[]2X(S()ATSaTSf()()。S2f22XX解(sz)(sz)(sz)H(s)H123(sp)(sp)(sp)0123s(s2j)(s2j)HH(s3)(s1j3)(s1j3)00[(s2)1]2(s3)[(s1)9]2s4s5s32H()H(s)H0s35s16s2ss451ss2limHH551610001ssss235s20s25s32H(s)s35s216s(s)(s)()Gs解H1(s)F(s)G(s)1(s)F(s)。在s在sj()1()()GjAjFj()，可在GjjjsjGj()G(s)1(s)F(s)n由snzp()F()(1j点变到时，在平面中的奈奎斯特图顺时针方向围绕(nn)nn(1(nn)j点zpzppzG(s)1(s)F(s)s在G(s)s在(s)F(s)没sG(s)sn0p1j0环特性稳定条件下的奈奎斯特图顺时针绕()点之次数等于系统函数分母G(s)1(s)F(s)在sH(s)(1j0)K()F(),K01j0(j0)F(jK0BK当,0O当2由0从0K0(1j0K()F(),K0(2KKAF12)222)20,0K当K1AF220OC由K0(1j0)解1t)1t),ft)sin(8t)f212(t)f(t)f(t)则f12t)[1tt)）fft)ft)ft)ht)ft)ht)h(t)1111Ut)Ut1)]U(t)U(t1)]tUtUtttUt)Ut1)]U(t1)U(t2)]U(t2)U(t3)]Ut)Ut3)(1)[()(1)](1)(1)yt)ft)ht)Ut)Ut3)]U(t)U(t3)]12tUt)t3)Ut3)(t6)U(t6)yt)sintt)sintt)t)0tt)t)t0t0t0g(k)(k2)3g(k1)2g(k)e(k)(1)(2)g(k)5g(k1)2g(k)y解(n)ny(n1)y3y(0)0,y(1)1,y(2)219,y(3)3y(2)3633y(4)4y(3)10031y(n)[n(n1)]u(n)2212s(s2s1112j(s)2(s)5(s)2(s)52200002e2ss4s2021s1arctg(42)22s(s(s2s5)221041t)R)2cosR故1X2xf关键是求状态转移矩阵t)(sIA)1。(s)(sIA)(0)11012s12sIAs1s40114s42s42adj(sI)1ss5s6s5s6s5s622(sI)故1(sI)1s1s5s6256ss22()()t()(1sIA)(0)st11zi22237eeeeee23t2t3t2t3tteeee3t257e3t2t3t2e2tt()(0)()(0)tt)teAtzit)2ee22ee2t3t2t3t(t)eAt(sI)11eeee2t3t23ttt)1222AA是14ecIcAAt0112602AAI142,3为12232ce2tcce2te3t010ecc3eec3t2t3t01110122e2e3te2t2te3t故ecIcAcc01142eeee01012t3t23ttt)(sI)112ee37eee2e3t2t3t2t3tt()()t())tteeee257e232t3te2t3ttt()r(t)1Rs求。(s)r(t)sRR(s)sr)r)3())2()0srRss2sr(0)r(0)3(0)rs543R(s)s23s2s23s2s1s2rt)(s)ee,t0R2tt11et)E(s)s1sR(s)r)2R(s)E(s)r(0)E(s)211R(s)故s2s2s2s2s1R(s)2ert)(ee)e(et0故12t2t2tttSa(1)jSa22222SaSa(2)2cos222222(t)t)t)及将edr(t)、rt)dt00到t0r(0)r(0)、00到将et)Ut)drt)2rt)Ut)dt()00(0)r(0)0tr。将et)Ut)drt)2r(t)(t)dtd0到0r(t)t)rt)dtd()()()()中将含有冲激偶trttrtdtUt)Ut)00()的t(到(t)r0t0在drt)t)bUt)dt00到rt)aUt)0Utdt()0。0()()()atbUtaUtt()2a3,b6r(0)r(0)33(0)r(0)3U(t)故r(t)eU(t)将e3tdd2rt)3rt)2rt)eUt)t)e3t()()Utt3t200从到0t0在d2rt)t)bUt)2drt)aUt)则dtrt)0Ut)(t)00r从到()()()()3atbUtaUtta1,b3r(0)r(0)1,r(0)r(0)13故teu(t)t6022,312()C(2)C(3)ykkkzi12y(0)2,y(1)1ziziCC212CC1125,C3C121H(g)q25q611q1q62q23q3111h(k)(k)U(k)kk623y(k)e(k)h(k)111U(k)(k)(2)(3)U(k)kk6231112113k1k1313U(k)621211112(3)U(k)kk621621(2)(3)U(k)kk2215y(k)y(k)y(k)U(k)kk22f)sTt)）rt)ft)ht)ft)h(t)）rT)fT)ht)f)hT)f)s)）rT)ft)st)22021,212y(k)CC(2)kzi12CC012CC1121,C1C12(k)[1(2)U(k)故ykziq21H(q)232q1qqh(k)U(ky(k)e(k)h(k)U(k)U(kk1)U(khy(k)y(k)y(k)y(k)(12U(k)(21)U(k1)2(21)U(k)kkkzizs解z(2acosza)(ae)(zae0)22zH(z)b0z(2acosza)(zaezae)j0)(21211j00H(z)zae，zaej0012H(z)zae,zae11jj00121~zzT或slnzT1ssTslna和slnajslnaj和sajln10201020从j(k)(k)y(k)h(k)当f51h(k)h(k1)h(k2)kk()(2)66h(k)(k)(kh(k)与。(k)()hk151h(k)h(k1)h(k2)(k)66111510h(0)h(1)h(2)(0)1取k66111(1)h(2)0h11h(0)11(1)0h1h(0)1151EE026611311,ph(k)A()A()pkk2231211211h(1)A()A()01123112h(0)AA11123,A2A1211h(k)3()2()k0kk23111h(k)[3()2()U(k)kk231(()hk）k211h(k)h(k2)3()2()k2k2k2232111h(k)[3()2()U(k2)k2k2232h(k)为1111h(k)h(k)h(k)[3()2()U(k)[3()2()U(k2)]kkk2k2232312解0.8,,TTTcps111H(j)1011(/)2N2NapPC11H(j)101(/)2N12NN4.88845阶assc3.0277N4.8884N，2221.453126.1554tan,tan,tan,pcs2T22TTTTTcps111H(j)101(0.72655)2NaP2N1PC11H(j)101(3.0777)2Nss2N1sCN解NN2.11493当x(n)u(n)z2az1zY(z)(zaza1za1az1a1y(n)au(n)nu(n)a1a1当x(n)ejnz2azejzY(z)(zaze)aezaeazejjjaejy(n)au(n)neu(n)aeaejjy(n)H(z)(k)(k)e2h(k)h(k(k)(k210121kh(k)CCk1h22h(k)h(k1)(k)(1)(2)112h(k)h(k1)(k1)22(k)h1h(0)2即C=211kh(k)21U(k)2(k)h2h(1)12即C21kh(k)22U(k1)故2h(k)h(k)h(k)1211kk2U(k)2U(k1)220,x(t)。Tn2T1xt)sintdtsinntdtbnT0011cosntn(cos1)tn02奇数为偶数n02T1()1xtdtdt0T00R1H()1RjLj11H()11jn1e1()2Y()bH()n21e为奇数n1()n20为偶数n0ac21n0,YH(j0)2021n1,Ye112ejn2,Y0221nYejarctg3312z(z)H(zz2s1s2112(s(s422t)解f2E2E()fttttt112222112E2Et12t()F)eeje1ejjj2222114Etcoscos12214EF)122218E))sinsin1124413r4F)1当在112411eeeet2ttteAttetett4365AR)ft)ft)dteut)eut)dta(t)eedtu)e2()edtu））0111u)e()ueea)2a2a2a1R)limT/2ecostut)cos(tut)2T00TT/2ee22lim/2(2t)])}u(t)u(t)TT4000TT/2解K10s2s2K(K即p2K0,s2KK2s所(ssK(K1,p31和ps12s3K从03s1ddsA(s)F(s)0s2s21(s)F(s)0K1得s2K1分支再上、下分开并趋向于。(ppp)(zzz)12n12mnm013202(p为极点，z)ijl和l1,3)。nm222）xt)xt)11xt)2x(t)f(t)22xt)3x(t)f(t)33yt)xt)xt)12t)100xt)0x11t)020xt)1[ft)]即x22()003()1xtxt33t)x1yt)[110]xt)2()xt31(s)C[sI]BD）H1s2故h(t)eU(t)2t100s11(s)[sI]001）1s2003set00t)[(00se2t00e3t(t)C(t)x(0)(eeU(t)故yt2tx64sinTsinT)Tn(1)ISa2nej2T2nI2I2222;357I42(2);22244444I2(3)0.333I;;0.083I224t)hy(t)sintU(t)h(t)）fdd2tUt)tUt)(t)tUt)2d2t)tUt)tUt)））2dyt)2d2t)ht)f22dyt)2d2yt)sintUt)ht)sintUt)h(t)ff22d2sintUt)sintUt)ht)2dyt)2yt)ht)ht)ff2h(t)y(t)(t)(t1)(t2)。ht()fht)t)hththth(t)()()()1123()(1)(1)(1)ttttht()3()(2)(1)tttht()3ttht)ht)(t)(1)(2)]3yt)t()(1)(2)()(1)(2)]ttttty(t)ff(s)C(sIA)BDH1(sIA)1s221sIA0s2014sAs(ss2(s2)(s22s(s2s4(sadj(sI)sIA1(sI)0(s201(s2)(s1)2246(sss2故H(s)C(sI)BD1(s2)2s4(s2)0s11000(s201(s2)(s2246(2)1sss2s2100(s1)22s21s2(s2)(s2(s2)(s2(s2s21(s)HH(s2)(s(s22(s)(s)列写系统的微分方程，不应按零、极点已抵消的H来列写，而应按s2H(s)(s2)(s2dyt)dyt)dyt)det)32452yt)2et)32MNMNN33及。012M(BAB)1242149012detM12410149故(M)3,MC100N2213422100detN2210342N3即可得到第二列，(N)2N1a2;2121U1;jaaU(4)eaaa11e}）t()ssss12s2s1）{sint2cos}s1s1s122211dte}（3）2tds(s2)(s2)212t);2ft)cost04n3(1)S122n1nT2TTejej)22T222222ej)j)1K))H(e)jeKKj))1KK2)j21H(e)j1K2Kcos()2)K)arctan1K)zK0,H(z)1zKH(e))0(e)HjzK0.5,H(z)z0.51H(e)j)0.5sin()10.5cos())arctan解()0RXY解11Rs(RsL)RsLCLsC1Z(s)R1s2ssCLLCRLz1故R1s0s2LLCR4R2jLCLR1R2L2p1,2j2L2LC42若Z(s)RLz3①②13RRe(p)22L1111R2Im(p)③④2LC4L1,22RK(z)LC1Z(j0)1又1pp12LC11,LH,CFR解310(t)u(t)u(t1)u(t2)[u(t)(t1)][u(t1)u(t2)]）f4sin[attsintt)f[attft)()ft（2）ft0tt)5a05t00）dt)[esintut)]e(costsintut)2esin(t)u(t)）f.ttt46dt(t)(1e2eU(t)h(t)(2e2eU(t)ru2tt2t2t22(cos2sin)ej1021解1,2y(n)(CnC)(1)hn12y(n)D3np1(n)将ypD32D3D33nn1n2n1119D1619y(n)y(n)y(n)CnC)(1)3nn16hp12将y(y091(CC)(03129C0239C,C41612399y(n)n(3nn4V(s)V(s)V(s)(s)H03RE(s)E(s)1n(s)E(s)E(s)V323n1RsV(s)E(s)E(s)1s2RRsC1s1s2故H(s)2s22s212H()Hs()22sjjp2z2j(t)v(t)v(t)0vV2301E0~180于V20求et)cos(2tV(t)p2，e2tt1j221H(j)e因j2j222211vt)cos(2t90)sin(2tV故220(k)by(k1)by(k2)ae(k)ae(k1)y1201解（1）f1(t)f(t)2[ft)ft)]EESa()Sa()（2）1222121212解s11R(RsL)sRsLRCs1sC1CLCZ(s)R1LCs2RsLss2sCLLC1RsCLRR21RR21ss2L4LLC2L4LLC22Rz1LRR21RR21Pj,pj2L4LLC2L4LLC1222R2z31pj1p2L2RL33RL①R1.5即12L30②LC1111R24LLC42(jZ(s)R1③又Zs0R1LH由31CF解s(RsL)I(s)sMI(s)E(s)12sMI(s)(RsL)I(s)012(s)I(s)2Rs(LM)Rs(LM)(s)V(s)(s)Rs(LM)Rs(LM)R2t)t)当eE(s)1，V(s)Rs(LM)Rs(LM)RR/2R/2LMLMRRssLMLM11RRRt)ee()utttLMLM2LMLMR1当et)ut)E(s)，sV(s)Rs(LM)Rs(LM)R1212RRssLMLM1RRt)(eeut)()ttLMLM2Ra1(1)A0a100(2)A044010T2和Tuu12100a1）A044）A0a010解3s2H(s)2s3s1a2s2A1A2(2ss2s1s13s232sA11A21s1122s1S1t11H(s)2s1s1a1ht)eeut)0.5tanT()()(0.5hnhnTe)u(n)令te0.5nTnTaH(z)h(nznn1(0.5eez0.5n1ez1ezTT11n00.51T0.5H(z)1ez1ez1121z1z11z11s4H(s)将T1z1a1z11221z1H(z)121zz11321211z11z1zz)1132(1z)12(1zz)z)1211124zz12zz121z11z14s式11H(z)11zz1181411z11z11z11z14zz1297z153z1zz12ttsinsinsint22tht)tt111s）s(s5ss52211{}tu(t)s(s5232323）(s4)(s2)s4s233£{1}(eeut)4t(s4)(s23s63）(s4)(ss4s23s£16eut)eut)4t2t(s4)(s2)(e)x(n)(n)e1Xjm11njm(e)x(n)U(nU(neXj22neeeeeeeeee)j4j2j0jj2j2jj2j1ej1eej2j))eej2j2ej2j))(e)x(n)U(n)ee)Xjmnn33nn0111e10.5cos()j0.5sin()11X(e)j2)310.5cos()0.5sin()22ETTF(jja)cosSaF(0)0a222EF()b2cosTjTTFsin)(0)0T2bdx2t)43x12f(t)112dx243xft)2222dx2dxdft)(2)3x1ft)1xt2dt1dtdx23dxxdft)2ft)22dtdt2dt2d2xd2ft)dft)(3)9x23ft)1dt21dt2dtdx2dft)dft)29x2dt22dt2dtdx2dxdft)(4)2x3ft)11dt2dt1dtdx2dxdft)23x22dt2dt2dt1()Sa()22212[Sa()Sa()])22nkk1k1、2cc12151515uetcucUt2()()0utceUt()()0.2tckutA()utUt()10()CpCputututUt()u(0)u(0)0()()(0.2()tCCCt()C10ut()10(1eUt0.2)()而i)CCeU)tCCt1()1kuu))当C252CCt()3153535utCet()()0，即C53utceUtutAAc()(3)()0.6(t3)ChCptututut()[Ut](()()3Cu(3)u(3)10e在3CCutCeUt得c1.18()[](，t3iteUt(3)0.6(t3)()0.354而CN))解R02xNN))e0j022x11(),H12()H222N2)G)H()20)x22NN2edR)00j)y22eN2()j(在z处的留数)00z22NNe2ijea()0241(kk(k)x21x(k)31(2kk44)S))X222200t(1)u(t)EeUt)RRCt(2)ut)eetUt)1RCRRCEUt)(1etUt)t(3)ut)(1eRUt)etUt)]t(4)ut)[eRt(5)ut)costsinte1()2RRCtTtTt(6)ut)[(1eUt)(1eUtTeUtT)TR0K8/91t)t解f2211t,t2212()4ft2,()4t2tft1t12212t111122ttt2222t)sint有无穷多个根，分别为tkkfk1,k为偶数()cosftt1,k为奇数kttk()1则ftk)()ttkk(1)rt)(1teUt)2t1(2)rt)(2e1)Ut)[2e1]Ut1)2t2(t1)T11[2e2(t1)1]Ut1)T1[2e2(tT)1]U(tT)1)t)ft)求f2ETT2()ft()EtgtEtT2T2ETT2TTT()Fj[ee]2E[]Ejj2222T()()FjjFj12ETTF()()Fjj]22t)ft)求fE()ftt)t)tT)]TE()[1]jTFjjeT()()2()FjFjj11EEF()()Fj[1je]je]jTjT()2()TT22T(c)ft)G(t)Esin(t)2T11TF()G)e)211G(ej()TGej()T))]12112211(d)ft)Egt)sintTT1TF()ETSa()j2TTTsin1Tsin1Ej2Ej22SaTSa1122211TTTTTTT))2sin222221j22111111(z)H311zz124831y(n)y(n1)y(n2)f(n)48zz11(z)h(n)()u(n)()u(n)Hnn121424zz1z()u(n)n122zzzzz22zzY(z)H(z)F(z)()1214121114zzz(z)zz221211Y(z)2(n1)()2()u(n)()u(n)n1nn2222tt)1ht);yt)[ttyt)002tt)200解(s)Ha1H(j)1/1100.99763220acsJc11H(s)H(s)()Hj21T(s/j)a221T()22NNc1T(sj/)cos[arccos(/)]NsjjN1121ksinhsinhsinar2N1Nk12k1cosharsinhcosk1,2,N2NkN0.99763N2，将0.322450.77716ssj10.322450.777162j2N1H(s)(sj)(sj)(s)0.64490s2RRHLLRR1RasLL()()ss114[(s)0.64490s0.70795][(s)0.64490s22[(s)0.64490s0.70795][(s)0.64490s22[(s)0.64490s0.70795][(s)0.64490s22(s)(s)42[(s)0.64490s0.70795][(s)0.64490s22[(s)0.21574s[(s)0.21574s22[(s)0.64490s[(s)0.64490s22(s)0.21574s2(s)(s)0.64490s21(s)2(s)0.86084s2Z(s)1(s)0.42916sn14.66023s0.34856s0.1511()Zs1Z(s)n4.66023sn0.34856s0.15Z(s)Z()snnt)h()5()htht)()()ftdt)()()()()()()fttftfteuttdt()5()t()()hthteutt(t)Ae,t0h5t(t)设h1()5()()hthtt）11h(t)2()5()hthteut()）t22h(t)2h(t)h(t)12(t)h(t)h和12(t)h1(t)eu(t)h5t1(t)h2h(t)=+2(t)AeBe,t0即h5tt214BBet1ht)Aee,t05tt42()()()0httht在t22h(0)h(0)0221111A0Aht)ee,t05tt444421t)2ht)ht)(e7eut)）ht5t4121as11sa)aF(aF(asa)Fa()F(2a2aa1212SattSattSatt[({[()][])]c2c00c0cc解初值定理的应用条件是：F(s)F(s)(s)ft)f(0)[F(s)]f(t)F1000f(0)f(0)f(0)limF(s)000s）F(s)s）F(s)s0在处t)fs22s1(ss2)(ss32x2sf)f(t)1）s4ss632t0ssF(s)在ps1ft)1t)F5s9s52F(s)11F(s)(ss2)(s05s9s5s32f)f(t)(s)]5故(ss2)(s0t0ssF(s)p1,2,3ft)spp123即f()limft)limsF(s)0tt02s12s1)ft)s0）fs(ss(sst0sxF(s)fp1,2sp0s0p123t)2s1s(ss2s11f()ft)s(ss2ts0s0s22s3s32s23sf)ft)s1）s32s4s42ss4s432t0sss22s3s2s3F(s)即F(s)在sjs3s24s4(ss2j2ft)F(s)1e2s1e02tf)ft)s2(ss422t0stF(s)11ft)[F(s)]cos(2t)]ut)[1cos(2(tut2)144(0)0fF(s)1jft)ft)的在st)()）fGt22则200G(t)200Sa(100)200故1Gt)Sa(100)2001Sa(100t)2G)G)200100100(rad/s)s或10050f(Hz)ss50100f2f2(Hz)Ns1TNsfN()Fa8E()T)t)F)T44a212ET)T)TFF)()n2tTT2nan12F)FTnn()FbTcos2ET2F)bT1212Ecos()2E4)FF()(n14n2n2Tnbn1TcfcFf1mf2fmsmff0.5kHzs2mFf2cffffmcsmf0.5kHz,Fm1fffcSmf又fmcF1解zH(z)(n)(1)u(n),hnz10z1z10z(z)Xz15z5zY(z)H(z)X(z)z1z1y(n)(1)u(n)n111111sV(s)V(s)sV(s)V(s)222222201a11122V(s)sV(s)022aV(s)kV(s)02kV(s)V(s)10s2(3k)s1V(s)kH(s)故0V(s)sk)s1123k0k3即当22202eeeet2tt2tAe13etee2tte2tN13(k)DFS[x(nx(nWx(n)ejk解Xk42ppppn0n02ejejk)3kk222x(0)4，x(1)2，x(2)0，x(3)2ppppt)utut解e222