經(jīng)典word整理文檔，僅參考，雙擊此處可刪除頁(yè)眉頁(yè)腳。本資料屬于網(wǎng)絡(luò)整理，如有侵權(quán)，請(qǐng)聯(lián)系刪除，謝謝！1sgn(t)(k)為f(t)(t24)(t)f"(t)_______f"(t)2(t)'(t)。f(k)h(k)f(k)h(k)______f(k)h(k)6,。H(j)_______H(j)Kejt0。()f4最高角頻率為。mmP22f(t)4cost2cos30tn1=2F(j)1122zz(2)(ttdt2(j)A)e,)圖64201234t圖h(k)khk(2),()(0.5)()k()hk。k12f(k)y(k)h(k)h(k)12圖h(k)(k)hkhkkk()()()(2)(0.5)[]()(0.5)(kkk2)kk212f(t)f(t)2????-2??-3?-10123n圖f(t)f(t)Fenej20t2ej0t22eje2tt24cos2cos20t0t0tj00nf(t)(t)(t()yt()tyt)202t圖(t)f(t)f(tf(ti)f(ti)(t)i0T(t)}()ytii0321t012345圖f(t)F(jSgnSgn)()ft。1F(j)2)g12gt)2Sa)2Sat)g()g)2222ft)Sat)三、綜合計(jì)算題（共20分，每小題10分）y"(t)7y'(t)10y(t)2f'(t)3f(t)f(t)e(t),y(0)y'(0)t由sy(t)x(t)yy(t)f；H(s)h(t)解：s2Y(s)sy(0)y'(0)7sY(s)7y(0)Y(s)(2sF(s)sy(0)y'(0)7y(0)2s3Y(s)F(s)s27ss27sss821Y(s)s7ss2s5x2y(t)2ee,t02t5txs2s32s31/41/312/7Y(s)F(s)s27s10(s27s10)(ss1s2s5f117yt)(eeet)t2t5t43f11eyt)yt)yt)ee,t0t2t5t43xfY(s)23s1/37/3H(s)fF(s)s7ss2s5217ht)(eet)2t5t33s2s3s12H(s)17s10s122F(s)Y(s)-3s1s1710y(k)3y(k2y(k2)f(k)k0f(k)(k),y(2,y(2)由zy(k)xy(k)y(k)f；H(z)h(k)。f(k)(k)(k5)若zY(z)zY(z)y(}z2Y(z)z1y(y(2)}F(z)3y(2zy(2y(2)4z4412Y(z)x13z2z13z2z1z12z121211zy(k)[4(4(2)(k)kkxzF(z)111/61/24/3Y(z)13z3z13z3z1zz)z)2z)f12121111z113Y[k][((2)(k)kk624f781y(k)y(k)y(k)[((2)(k)kk236xfY(z)112H(z)fF(z)13z2z1z12z1211zh(k)[(2(2)(k)kkf(k)(k)(k()ykx()()Hz若hkT(k)(ky(k)y(kff113113[((2)]k()[(((kkkk5k5624624y(k)y(k)T{kk()(x178113[((2)(k)[((2)(kkkk5k5623624長(zhǎng)沙理工大學(xué)擬題紙2sgn(t)(t)(k)(t)(k)為一、填空（共30分，每小題3分）t)yt)tft)2X(0)2f(t)13(2tt)(t2)22021(2(42)_________tdt(2(42)dt1tttdtK0=。fkf(k)2(k)(k()5()()fkfkk1212f(k)f(k)12f(t)y(t)Kf(tt),(K,t為常數(shù))f00。H(j)=h(t)H(j)Ke(t)K(tt)h。jt00f(Hz)mf(t)y(t)f(t)f(2t)若11T(s)Tmax2f6f隔。T為mm1F(s)=(ss()Fj21H(z)122zztttdt(2)(32F(jAe3A)),)ft()j二、計(jì)算題（共50分，每小題10分）1ht)Sat)f(t)3cos2t,t二、解：1/31H(jhtg)[()363T{cos(t)}()cos())Hjt0000f(t)3cos2t,t1T{ft12t,t3f(2t2)f(42t)f(2t1-2-1012t-1圖f(2t2)f(42t)f(2t2)f(4t)111f(2t2)f(4t)222tt212t(412)/2t(4t/2311222f(4t)f(4t)13t012f(t)F(j)。ft)202t圖f(t)(t)ft)f與121())tft)2tt(2)[(2)]jf(t)F(j)12ej2F(jt)()j1F(jFT[f(t)]6Sa2))222ej2F(j)FjFj()())6)2j12f(t)f(t)32tt02202圖h(k)[(1(0.5)1(k)kkz1232.5z1H(z)1z10.5z11.5z0.5z1112z1.5z0.5zY(z)(32.5z)F(z)121fzy(k)1.5y(k0.5y(k2)3f(k)2.5f(kx(k)y(k)1-11zf(k)ay(k)2-b圖x(kax(k)f(k),x(kbx(k)f(k)1122y(k)x(k)x(k),y(k)x(k)x(k)112212(ka0x(k)1xf(k)11xkx(k0b()122y(k)11x(k)11y(k)211()xk2三、綜合計(jì)算題（共20分，每小題10分）31y(k)y(ky(k2)2f(k)3f(kk048f(k)(k),y(y(2)1在zh(k)H(z)；y(k)x；y(k)f；y(k)?.z31Y(z){zY(z)y({z2Y(z)z1y(y((23z1)F(z)483411y(z1y(y(2)23z881Y(z)F(z)31311zz1zz12124848Y(z)23z1H(z)f3111F(z)1zz1z1z12114824z11h(k)F1[H(z)14()]k()kk24z311131y(z1y(y(2)z19/45/8488843Y(z)31111x1zz1zz1z1z121211484824取z9151y(k)[()()]kx()kk4284z23z23z114/3140/311Y(z)F(z)31311zf11zzzzz)1z1z1212111484824取z11y(k)[16()()(k)kk2343f11y(k)y(k)y(k)[()()(k)kk4243xf1140[()()](k)(k)kk4243著kkz1/z1/412f(t)F(j)DE和F，()t(tnT),T0.02T。nH(j)1H(j)1CDEFyt)ft)Btt)TF(j0.1)ABE和FF(j)),nB000Tn11F(j)()FjFj())50Fn100)FnTCB0nnF(j)F(j)H(j)DC11F(jF)[)F2EDDF(j)YjF(j)H(j)()FE2長(zhǎng)沙理工大學(xué)擬題紙3sgn(t)(t)(k)(t)(k)為一、填空（共30分，每小題3分）f(t)y(t)Kf(tt),(K,t為常數(shù))f00H(j)=h(t)(j)Ke()()jt0。HhtKtt。0f(Hz)mf(t)y(t)f(t)f(2t)若11T(s)。TT2f6f隔為maxm2(2(42)_________tdt(2(42)tdtdt1tt1K0=。f(k)2{kk()(()5fk()()fkfkk1212f(k)f(k)12t)yt)t2ft)X2(0)f(t)13(2tt)(t2)2202s3se22F(s),(Re(s)0),=。s(s9)f(t)2f(t)(2cos3te2sint(t)yt)ee5()d,(tt。tY(j)=2e4ej21ej24Y(j)25()7jjjj22zz2F(z),(zz=。(zz()fkf(k)z1[F(s)][2((k)kkejt0H(j)m=。0h(t)111ht)Hjedt()jteedtjte(dtSa()]mttjtt0)jt0m0mm二、計(jì)算題（共50分，每小題10分）f(t)F(jSgnSgn)()ft。1F(j)2)g12gt)2Sa)2Sat)2gg())2222ft)Sat)h(t)thte(()(2),()thte()t3t2t123h[k]2yt)h[k]3圖ht)[ht)t)][ht)httte((([(2)(te2tt3t123(te(2)(()()tte(2)()()tte2tttte3t2t3te61e3(t3))te2(tte(((2)()te2tt3t32f(t)g(t)f(t)g(t)和和gt)21101t0t圖f(t)g(t)和ft)gt)t0123圖2s7H(s)253ss2s7s12H(s)15ss122yt)ft)-217s153圖()()()()xtxtxtft()5()xtxt，12212yt)7xt)2xt)12f(t)T(t)最高角頻率為mfTft()sf(t)。mft)sft)Tft)tft)T/2/2TT圖f(t)T1()4F(n),220T2T4T0nn0ft)Tf(t)FeSa2(n0)e0tt0T4Tnnnf(t)TF(j)TF(jT)Sa2(n0)nT40nf(t)f(t)f(t),1sT(n0))FnF(j)()FjFj()Sa2T4sT0nTF(j)()Fj()ftT從0msmsf(t)。三、綜合計(jì)算題（共20分，每小題10分）y"(t)7y'(t)10y(t)2f"(t)f(t)f(t)e(t),y(0)y'(0)t在sh(t)H(s)；y(t)xy(t)ff(t)e(1)(tt若、。解：s2Y(s)sy(0)y'(0)7sY(s)7y(0)Y(s)(2sF(s)sy(0)y'(0)7y(0)2s1Y(s)F(s)7722Y(s)xY(s)fY(s)21s13H(s)fF(s)s7ss2s52sh(t)(e2e5(t)tt4s5/3/3Y(s)s7ss2s5x25yt)exe5t,t02t33s2s12s10.2510.75Y(s)F(s)s27s10(s27s10)(ss1s2s5fyt)(ee2e5t)tttff(t)e(t1)(t()y(t)若，則系統(tǒng)單位沖激響應(yīng)、系統(tǒng)函數(shù)Hsxyt(e(e2(e5(ttttff(t)F(j)Ey(t)f(t)與1H(j)1DCBEyt)ft)A80100t)t)2圖D和EF(j)FTt)]100)100)]A11F(j)FjFjF()()[100)100)]F2BAF(j)FjHj()()CB11F(j)F[100)F100)]2DCCF(j)YjF(j)H(j)()ED2Y(j)F(j)AD和E與11Y(jFj)()yt)ft)44即。長(zhǎng)沙理工大學(xué)擬題紙4sgn(t)(t)(k)(t)(k)為一、填空（共30分，每小題3分）1e3t1e(dt3tee(________dt2t2t2t4t2k(){1fkh(k)(k)(k4)1kf(k)h(k){1為。y(k)f(2k)f(t)cos(t(t)(t)]'()ft若，則其微分=。f'(t)sin(t)[tt()()]()()tt,4tF(j)g()ft)84_________F(j)t=。f(t)(t(t)tF(j)的頻譜=。tSaFT{[(t(t)}100)100)Sa1g(k)()(k)k2已知一離散時(shí)間系統(tǒng)的單位階躍響應(yīng)，計(jì)算該系統(tǒng)單位脈沖響應(yīng)11h(k)g(k)g(k()k()()(kk1kh(k)22=。為基頻)f(t)24t)3cos(20t),(t)f(t)若，則的平均功率033PF2n222()()16.522222_________22。nttyt)f()f()f(t)42若最高角頻率為。mTmh(k)[((0.5)(k)k1k1若離散系統(tǒng)的單位脈沖響應(yīng)，則描述該系統(tǒng)的差分方程為y(k)1.5y(k0.5y(k2)3f(k)2.5f(k。二、計(jì)算題（共50分，每小題10分）f(t)r(t)t(t)。f(t)1034t圖(t)r(t)f(t)用和；f(t4)f(t)r(t)r(t(t2)r(trtt(4)(2)將f(t4)f[2(t2)]f(t4)f(2t)f(2t)f[2(t2)]11121.5ttt00101()(kk(k2，f(k)(k)(k)()yk。1()(kk(k2，f(k)(k)(k)()yk。f(t)H()j1-0-6-5-4456圖gH(j)[gej25)]22gt)2Sa)2Sat)g()g)即2221Sat)g)22Sat)5tg(g222Sat2)t2)[g(gej2222ht)Sat2)t2)f(t)53cos2tcos4t,ty(t)H()133圖T{cos(t)}()cos())Hjt0000)0()ftT{f(t)}5H(j0)3H(j2)costH(j4)cost52costt，f(t)(t)(t()((yttt所y(t)g(t)gg(t)1t01圖gt)f(d)tyt)y)dd]ttttgy(t)210t11圖三、綜合計(jì)算題（共20分，每小題10分）y"(t)5y'(t)6y(t)2f'(t)f(t)f(t)e(t),y(0)y'(0)1t由sy(t)x(t)yy(t)f；H(s)h(t)1()[2)Hjgg2221Sat)g)2即11Sat)sin(3t)[g(g2j2211jSat)sin(3t)[gg222sin(2t)j2)2)]jsin(2t)2)2)jth(t)H(j)jjtht)[Sat)sin(3t)sin(2t132ht)[Sat)sin(3t)sin(2tSat)Sat)Sa(2t)tH(j)cos(t)H()cos[t)]由t)H(jt0000H(j，00.4cos(3)0.2cos(3)ttf(t)10.6cost0.4cost0.2costy(t)0.2cos(3t)p(t)T)()ftF(j)。p(t)F；np(t)p(j)f(t)；F(j)ppF(j)pTf(t)mAP(t)Tft)f(t)tT22Tp(t)圖p(t)F為n11AT/2/2Fft)edtAedtejntjntjntt/200()0TTTjnt/2nT/2/20sin(/2)nAnA,Sa00/22TnT0T0p(t)nApt)Saejnt0T2nP(j)為AnP(j)Sa)n0T20nf(t)f(t)p(t)p1AnF(j)Fj()*()PjSaFn)0T20pnTf(t)pF(j)可以看出，當(dāng)()Fjp0pmm長(zhǎng)沙理工大學(xué)擬題紙5sgn(t)(t)(k)(t)(k)為。一、填空（共30分，每小題3分）(t)(t2)](2t2)_______11t)t2)](2t2)t)t2)]tt22h(k)f(k)f(k)h(k)_______(k)*h(k)ff(t)sin(t)f(t)T0fHz=以s。()t。fkft()sinkf(k)=(tt)t，00。(t)()t'1j1jH(j)H(j)()j性=H()1)2arctan()H(j)e2)j，t()2。tsint2111)d2dtg2dt21h(t)ht)dt。的最高頻率為。。(rad/s)2(rad/s)f(t)()f2tsm1()(k)k411k1kh(k)g(k)g(k(k)(k。44。f(t)sint(t)(t/2)]f'(t)tf'(t)cost(t)(t/2)](/2)二、計(jì)算題（共50分，每小題10分）h(t)f(t)y(t)y(t)f(t)1-h(t)20t01t12圖y(t)f(t)h(t)y(t)22t013-2圖f(t)f(0.5tf(t)若-21-3t012圖f[0.5(t2)]f(0.5t圖f(0.5t將f(t)(t)f2(1)11tt-3-2-1(2)06420f(t210t8642z22z2s1H(z)z33z2z12z2H(z)13z2zz1232F(z)Y(z)2z132y"(t)5y'(t)6y(t)f(t)4f'(t),t0y(0)y'(0)3f(t)e(t)t。sy(t)x(t)y由sf。ss2Y(s)sy(0)y'(0)5sY(s)5y(0)Y(s)(4sF(s)ssy(0)y(0)5y(0)4s1'Y(s)F(s)s25s6s25s6ss25s6s1Y(s)3s2xy(t)e3t,t0xs4s14s11/4313/4Y(s)F(s)(s2)(sss1s2s3s25s6f113Y(t)ee2e3(t)ttt44fH(s)H()2。j02圖H(s)h(t)g(t)；。H()H(s)s(s2)為2s(s2)3H(s)K2(ss(sss1s3h(t)(t)ee315()ttts2s(s2)135G(s)H(s)t(ssss1s3g(t)(ee(t)t3t三、綜合計(jì)算題（共20分，每小題10分）y(k)3y(k2y(k2)2f(k)f(ky(1/2,y(2)1/4,f(k)(k)由z。(k)y(k)xyf。H(z)zY(z)zY(z)y(z2Y(z)z1y(y(2)](2z1)F(z)3y(2zy(2y(2)2z11Y(z)F(z)13z2z13z2z1212z3y(2zy(2y(2)2z1312z11Y(z)13z2z13z2z1zx121211取zy(k)[(3(2)(k)kkxz(2z)F(z)2z1/221/211Y(z)13z2z3z2zz)1z12z1zf12121111取z11Y(k)[(2(2)(k)kk22fY(z)2z1H(z)fF(z)13z2z12zz212H()，c()j100cc圖計(jì)算該系統(tǒng)的單位沖激響應(yīng)h(t)；f(t)10.5cost0.2cos120t()yt。H()g)]et0cSat)g)c(t)12，ccht)ttt())())tc1ch(t)h(tt)(ttSa)80(tt)]100080()ft80y(t)0.2cos120(tt)0長(zhǎng)沙理工大學(xué)擬題紙6sgn(t)(t)(k)(t)(k)為一、填空（共30分，每小題3分）5((2________tdtt。51155((24)tt((2)(0.5ttt22t2551yt)[ft)f(tf(t)F(jR))jX)2Y(j)為。1H(s)_________s1_________f(t)=410t456-6-5-4-11圖kk0kk[](()()nnkkk0=。nn_。H(z)f(Hz)0f(t)f(t/2)已知信號(hào)的最高頻率，對(duì)信號(hào)取樣時(shí)，其頻率不混迭的最大取樣間隔11T2ffTmaxTmax=。為。0f(t)y(t)f(4t)ttyt)f()f()f(t)42若最高角頻率為_________。mTm1F(z)1(z)(z2)zmax(z,z)2f(k)F(z)()fk2的z，12二、計(jì)算題（共50分，每小題10分）h(t)f(t)y(t)。f(t)h(t)110t012圖y(t)f(t)*h(t)yt)1t0123圖y'(t)2y(t)f(t)y(t)(2ee(t)t2tsY(s)y(0)Y(s)F(s)y(0)1Y(s)F(s)s2s2y(0)1Y(s)Y(s)F(s)s2s2fx，y(t)y(0)e2(t)txf(t)ke(t)tkF(s)s11kkkY(s)F(s)s2(ss2)s1s2fyt)(keke2t)ttfy(t)[key(0)e2ke2(t)ttty(t)[2ee2(t)y(0)52ttk，y(t)y(0)e()5()tet2tt2xyt)(keke2t)ee2t()ttttf1NN1[k]f[kn]n0f(k)(k)y(k)h(k)1Nh(k)151N1h(k)(kn)kkkkk()((2)((4)]kk()(5)]5n0h(k)k014[k]115nk0s213s1H(s)s32s2yt)f(t)-21s1s132圖()xtxt()()xtxt()()()xtxtxtxtft()2()3()，，31223123y(t)x(t)x(t)p(t)13)()ftTF(j)。p(t)F；np(t)p(j)f(t)；F(j)ppF(j)pmf(t)TP(t)ATft)f(t)ptTTp(t)22圖p(t)F為n11A/2/2TFft)edtAedtejntjntjntt/2t/200()0TTTjnnT/2/20sin(/2)nAnA,Sa00/22TnT0T0p(t)nApt)Saejnt0T2nP(j)為AnP(j)Sa)n0T20nf(t)f(t)p(t)p1AnF(j)Fj()*()PjSaFn)0T20pnTf(t)pF(j)可以看出，當(dāng)()Fjp0pmm三、綜合計(jì)算題（共20分，每小題10分）6y(k)5y(ky(k2)f(k)k0f(k)(k),y(y(2)3zy(k)xy(k)y(k)f；；H(z)h(k)若zf(k)(k）Y(z)zY(z)y({zY(z)zy(y(2)}F(z)1215y(zy(y(2)F(z)1Y(z)65zz65zz1212z5y(zy(y(132z9/27/311Y(z)1165zz65zzx12121z1z1123取z9171y(k)[()()]kx()kk2233zF(z)11/21/611z31/2Y(z)165zz(65zzz)1zf1212111z112取z11111y(k)[()()]k()kk22632f1511y(k)y(k)y(k)[)()(k)kk2232xfY(z)11/211z21/3H(z)f1F(z)65zz121z113取z1111h(k)[()()]k()kk2233y(k)xf(k)(kh(k)H(z)若111y(k)[()k1()k1k(233f9171111()y(k)y(k)y(k)[()()]k()[()(kkkk1k12233233xfH(s)sc21z1sT1z1sTssH(e)jdH(z)d21z211H(z)z)1T1zST1zSd112X(z)Y(z)Tsz1z1）2X(z)Y(z)Tsz1）圖H(e)H(z)dd為zejsin()21ej2ej(eej222222(e)jtan()ejH2T1ejT2dSS222S2j2TdTSS0長(zhǎng)沙理工大學(xué)擬題紙（7）y(t)2f(t)11、某連續(xù)系統(tǒng)的零狀態(tài)響應(yīng)為，試判斷該系統(tǒng)特性（線性、時(shí)不變、穩(wěn)定ttt=。h(k)f(k)2,23f(k)*h(k)5,2為。fF0Fj011f。33e(t)jj0t00nnt1cos(t)0.4cos(3/2)）000)0.4cos(3/2)1cos()0.4sin(3)t2jf(t)et(t)4j22=。f(t)F(j)F(jt)。f()；g(t)。。d。。、二、計(jì)算題（共50分，每小題10分）1F(s)se2)Re(s)0f(t)f(t)s1111(tnT)(s)t)F1eRe(s)0ss1e2s，，）n01(t2n)1e2s2令Tn0tnf(t)(t)*(2)(2)tnn0n0???t02468???圖H(j)H(j)1024圖h(t)；f(t)10.6cost0.4cos3t0.2cos5t,ty(t)。1()[2)Hjgg2221Sat)g)211Sat)sin(3t)[gg2j22即11jSat)sin(3t)[gg222sin(2t)j2)2)]jsin(2t)2)2)jth(t)H(j)jjtht)[Sat)sin(3t)sin(2t132ht)[Sat)sin(3t)sin(2tSat)Sat)Sa(2t)tH(j)cos(t)H()cos[t)]由0000t)H(jtH(j，00.4cos(3)0.2cos(3)ttf(t)10.6cost0.4cost0.2costy(t)0.2cos(3t)h(k)h(k)(k3，1h(k)0.5(k)k。2h(k)y(k)f(k)1h(k)2圖h(k)[h(k)(k)]*h(k)h(k)*h(k)h(k)．12122h(n)h(kn)h(k)212nk10.5nkn((0.5()knkn0k10.50.5(k)knn0(20.5)k(0.5()kkk1F()x(t)f(t)x2t)f(t)，，F(xiàn)(j)dF(jf(t)；2sin()jd2。，令1t。1t0由f(t)F(j)()2(f't)2tgtgt1gt)241設(shè)2113gt)Sa()ej3g4442442411；。再根據(jù)傅立葉變換的微分性質(zhì)可得：22ej2ej4()2jFjSaSae444F(j)[2Sa()Sa(ej22224010320F222241Fjdf1221Fj2d()f2tdt()0044)230j22ft)gt)2F(j)Sa)ej2212())j222F(j)Sa)ejd[ft)*gt22t0113[f(t)*g(t)]f)g()df)d2222t02321)4)fdd005、如圖所示連續(xù)時(shí)間系統(tǒng)，其中延時(shí)器延時(shí)T秒，理想低通濾波器的頻率響應(yīng)為：H()g)e01ccth(t)）cctt)]()()c0c，111ht)[ttSa)]cc0c0ft)Sat)F(jg2)()())gee0]f2c當(dāng)cY(jg)eeg]))ege(jTjtT)0f222y(t)(tt)Sa(ttT)f00ttttT(){((cc0c0c32ejH(j)0f(t)()tnTT4/30f(t)0nf(t)F。F(j)nf(t)y(t)。。3T4/3020T01343T323F0ft)ejdtnttejntdt22322T04nT023333F(j)F)n)n222n）nn3H(j)g)ej243333Y(j)F(j)H(j))))]g)ej2232232433399)()ej)g(0))()]ggej4422224443233)))ej]ej442232433324333))]))])j222221333t)))2221333t)))j1222)323334y(t)t[cos(t)sin()]422一線性時(shí)不變離散時(shí)間因果系統(tǒng)的直接型模擬框圖如圖所示，輸入已知f(k)4(k),y(y(2)2kZ4F(z)()Yzz132y(k)x(k)yy(k)f；H(z)h(k)zX(z)F(z)3X(z)2X(z)221X(z)z1X(z)121X(z)F(z)z32z21z4z32zY(z)(z4)X(z)F(z)21即(z32zY(z)(z4)F(z)1或3z2zY(z)4z)F(z)121y(k)3y(k2y(k2)f(k)4f(kzY(z)zY(z)y(z2Y(z)z1y(y(2)]4z1)F(z)3y(2zy(2y(2)14z11Y(z)F(z)Y(z)Y(z)13z2z13z2z1212xf3y(2zy(2y(2)2z75zz11Y(z)13z2z13z2zz1z2x1212取zy(k)(52(k)kxzf(k)4(k)kz414z5zzz1Y(z)F(z)13z2z3z1z23z4f12取z5y(k)(24(k)kk33fy(k)(4(k)k33Y(z)14z1zzH(z)56fF(z)13z12z2z1z2取zh(k)(562(k)kx(kx(k)12x(k2x(k)3x(k)f(k)212即(k01x(k)0xf(k)11x(k23x(k)122y(k)x(k4x(k)2x(k)7x(k)f(k)2212或(k)xy(k)27f(k)1x(k)2長(zhǎng)沙理工大學(xué)擬題紙8sgn(t)(t)(k)(t)(k)為一、填空（共30分，每小題3分）。h(t)(t)(t7、已知一連續(xù)時(shí)間系統(tǒng)的單位沖激響應(yīng)，其系統(tǒng)單位階躍響應(yīng)gt)h)drt)rttg(t)(t)t(t)r=。st)t0。H(s)Sa2t)9、對(duì)信號(hào)均勻抽樣，其頻譜不混疊的最小抽樣角頻率為400/rads。smttd,t2t2fyt)F(s)2()Yse2sf(t)F(s)，單邊拉氏變換Y(s)=s二、計(jì)算題（共50分，每小題10分）f(t)h(t)y(t)y(t)與f(t)1h(t)2t01t0解111ft)gt)gt)ht)2gt)222111，1111yt)ft)*ht)gt)*gt)gt)*gt2222111111112gt)*gt)[tt()(*[(tt)(2121211112[tt()(*[(tt)()]'(22211112[rt)rt)]*[tt()(222r(t2r(t)r(t1111yt)ft)*ht)gt)*gt)gt)*gt222211112[g(t)*g(t)][g(t)*g(t)]11tt111ttr(t2)2r(tr(t)r(t2r(t)r(tr(t2)r(tr(t)r(t]t2)tt(2)(3()((tttttt2或t1t2t1t1t0t0t1y(t)yt)21t02圖圖f(t)f'(t)ft(0.5和t24圖()ft(0.5ft．()ftt24(圖f(t)(0.5t)f22tt004224422f(t2t8064222圖f(t)y(t)g(t)z(t)z(t)的f(t)y(t)g(t)，，f(t)1yt)gt)11t4t-101013t-101(圖．設(shè)系統(tǒng)的單位沖激響應(yīng)為h(t)y(t)f(t)*h(t)y((t)f(t)*h((t)()()gtft()()*()ztgthtz(t)gth(t()*()()*fth(t()y(t()ty(t)(t(t(4)ttttz(t)y((t)r(tr(t(t4)(t((((4)t1ort4t11t33t42z(t)zt)2t24圖F(j)。f(t)1t23ft)1ft)．、和1111()((2)(2)(ft1ttttft11233ttt0220230((ft)F(j)設(shè)11ej2)cos(3)]2jj2j21)/2)/2)F(j22221即F(j))5()()22LcH(s)h(t)f(t)(t)y(t)？23s23yt)et)2t)2h2，2f(t)y(t)h(t)H(j)H(j)f(t)sin(2nt2y(t)。n1gt)221t()())gg2Sat)g)Sat)g)。根據(jù)傅立葉變換的頻域卷積性質(zhì)有：2212t)g221)*))*[)2g2221[)*[)))]*[)))21))21212y(t)f(t)*h(t)f(t)*[())]()()*)tSa2tftftSa2t1t)Fj()))2而1())221jF(j))2nn(2](2]n11))2))]21t2jt2212(t)f(t)f(t)*Sat)2sint2y2n1。n1y(y(2)1，1nH(z)h(n)；y(n)f圖11y(n)y(ny(n2)f(n)4811Y(z)[zY(z)y([z2Y(z)z1y(y(2)]F(z)4811y(z1y(y(2)F(z)88Y(z)1111xf12124848111y(z1y(y(2)z(z)48888Y(z)1111224xzzzz12248412111f1zz124828Y(z)z2H(z)fF(z)(z)(z)3z11()()nnnnnx181nnn273f1()](n)y(n)y(n)y(n)[()()nn2734xf圖圖1H(e)jeejj1214長(zhǎng)沙理工大學(xué)擬題紙（9）一、填空（共30分，每小題3分）t)T[ft)]f)dtyf(t)H(j)線f(n)y(n)3y(n)y(nf(n)4tht)(j)為tH。H(j)g)200otherh(k)f(k)2,2。為f(k)*h(k)5,2h(t)(t)(t知一連續(xù)時(shí)間系統(tǒng)的單位沖激響應(yīng)，其系統(tǒng)單位階躍響應(yīng)gt)h(drtrt)()(tg(t)(t)t(t)r=。ttd,t2t2fyt)F(s)2()Ys。e2sf(t)F(s)Y(s)s=2jF(j)f(t)et(t)F(j)4j2t22=g(t)二、計(jì)算題（共50分，每小題10分）。ft)ft)和：12ft)的矩形寬度1sT2s1EV（1ft)22sT4s3EV）ft)ft)和1121ET/2f(t)edt/2EedtSanFjntjnt0002TTTnT/2/2(/)sf500kHz06）或；01B(sB1000/)6或；1FSa()12215(/)s250kHzf5）或；001B106(sB500/)或；3FSa()2321；。f(t)f'(t)ft(0.5和2t024圖()ft(0.5ft、()ftt24(圖f(t)(0.5t)f22tt0024422f(t2t6422圖H()40，[k]z))z0圖kz(z2)H(z)(zzH()44k24z(z2)zzzH(z)2()akk(zzz1z3za得h(k)((k)kkH(j)H(j)1-4-2024圖h(t)；f(t)10.6cost0.4cos3t0.2cos5t,ty(t)。1()[2)Hjgg2221Sat)g)2即11Sat)sin(3t)[g(g2j2211jSat)sin(3t)[gg222sin(2t)j2)2)]jsin(2t)2)2)jth(t)H(j)jjtht)[Sat)sin(3t)sin(2t132ht)[Sat)sin(3t)sin(2tSat)Sat)Sa(2t)tH(j)cos(t)H()cos[t)]由t)H(jt0000H(j，00.4cos(3)0.2cos(3)ttf(t)10.6cost0.4cost0.2costy(t)0.2cos(3t)i(0)1A,u(0)V,R1.5,L0.5H,CFLcH(s)h(t)f(t)(t)y(t)？SsH(j)232ss；h(t)3(2e2e(t)tt12SSs2)3Y(s)2(s23s2)2(s3yt)et)t2三、綜合計(jì)算題（共20分，每小題10分）1、一線性時(shí)不變離散時(shí)間因果系統(tǒng)的直接型模擬框圖如圖所示，輸入已知f(k)4(k),y(y(2)2kZ4F(z)[k]()Yzz1-+32圖y(k)x(k)yy(k)f；H(z)h(k)zX(z)F(z)3X(z)2X(z)221X(z)z1X(z)121X(z)F(z)z32z21z4z32zY(z)(z4)X(z)F(z)21即(z32zY(z)(z4)F(z)1或3z2zY(z)4z)F(z)121y(k)3y(k2y(k2)f(k)4f(kzY(z)zY(z)y(z2Y(z)z1y(y(2)]4z1)F(z)3y(2zy(2y(2)14z11Y(z)F(z)Y(z)Y(z)13z2z13z2z1212xf3y(2zy(2y(2)2z75zz11Y(z)13z2z13z2zz1z2x1212取zy(k)(52(k)kxzf(k)4(k)kz414z5zzz1Y(z)F(z)13z2z3z1z23z4f12取z5y(k)(24(k)kk33fy(k)(4(k)k33Y(z)14zzz1H(z)56fF(z)13z12z2z1z2取zh(k)(562(k)kx(kx(k)12x(k2x(k)3x(k)f(k)212即(k01x(k)0xf(k)11x(k23x(k)122y(k)x(k4x(k)2x(k)7x(k)f(k)2212或(k)xy(k)27f(k)1x(k)2H(s)sc21z1sT1z1sTssH(e)jdH(z)d21z2111H(z)z)1T1zST1zSd12X(z)Y(z)z1z1）2X(z)Y(z)）圖H(e)H(z)dd為zejsin()21ej2ej(ejjej))222222(e)jtan()ejHj2T1ejTTST2dcos()2ej(eejSS222S2H(e)jtanjj2T1dTSS()0(k)為Er(k)r(0)。H(s)。h(t)et(t)tttcos(2)()，則系統(tǒng)是五階系3(5j)29t。，()*()tet2ax(n)eatX(z)a1zax(k)x(k)a(k)1k1，。(t)afnn？rad0Tf(t)f(t)y(t)f(t)的0100n100n88a0n。01,tt0,t1,tt01tgt)]*[(21[2)1)]*2Sa)=)]2sin]2sin2f(t)f(t)c)nFjFn0n/20T12[(e1e2Fft)ejntjntjnt(ejn04000tn22111sin(n)sin(2n)jntjntjnt0000n2n211000(kn2k,k0,2n/n)n/2),n2kk0,n/2n/2(k1/,3,5,()ftrads/Fj的000cnn4n13和，0rad/s320和32rad/s0y(n)nf(n)y(n)nf(n)f(n)y(n)nf(n)f(n)y(n)nf(n)和f(n)y(n)nf(n)；111222()()()()]()()fnfnnfnfnynyn121212f(n)y(n)nf(n)f(nn)nf(nn)y(nn)000y(n)nf(n)f(n)My(n)nf(n)nMny(n)nf(n)y(k)3y(k2y(k2)x(k)y(0y(2)0.5x(k)(k)y(k)，，。zY(z)z1y(z)y(zY(z)y(2)z1y(X(z)X(z)[3y(2y(2)2y(z113z2z]z2Y(z)(zzz2)121z1z2z6z12z13z2112y(k)z1Y(z[(((k)kk623三、綜合計(jì)算題（共20分，每小題10分）kx(k)k2q(kq(k)z1k3y(k)圖kkq(k)x(k)q(kQ(z)X(z)zQ(z)22ZX(z)Q(z)k1z12ky(k)q(k)q(k3ZkkY(z)Q(z)zQ(z)z1Q(z)33得k1z11k3Y(z)zQ(z)X(z)13k1z2kk1zz11Y(z)X(z)33kH(z)kkz1zz222，kkzzk222f(t)F(j)()Hjy(t)1()t)tTny(t)1Y(j)1；y(t)sY(j)sT(t)f22yt)Y(j)））11Y(j)sTTsH(j)）2c。11cs(t)(k)(t)為f時(shí)00t。0單位階躍函數(shù)(t)。(t)x(2t)。f2是。0，。tf)ft)*。()(1)tt()((2)fttt＝。fy''(t)2y'(t)y(t)f'(t)f(t)e(t)'H(s)h(t)5。；。圖y(k)5y(k6y(k2)f(k()ykf(k)2(k),y(1,y(2)1.(k)y(k)xyk且ff(t)esin(t)(t)，0t0h(k)a(k)k三、綜合計(jì)算題（共20分，每小題10分）H()，c()j100cc圖h(t)；f(t)10.5cost0.2cos120t()yt。f(t)F(j)AEy(t)f(t)與112CDBEyt)ft)A100808010015t)t)F(j)210圖長(zhǎng)沙理工大學(xué)擬題紙sgn(t)(t)(k)(t)(k)為一、填空（共30分，每小題3分）ft)3cos(4t)、sint'(t)3。＝。h(k)f(k)2,23。為0.5,0.5ej,eFTf(t)F0Fj011F0.2j,F0.2jf(t)。33ytfthtyt、。f(t)(t)y(t)e()(1)tt()((2)tt()yttft＝。ft0(ee)(t)2tf(t)(e2e)(t)t2tt；f(t)(2ee2(t)(5ee2t()tttt；f(t)(ee(t)(eet()tf(t)(ee()tt2t2tt2t。st)t。H(s)Sa2t)。ttd,t2t2fyt)2f(t)F(s)Y(s)二、計(jì)算題（共50分，每小題10分）=。x(t)cos(2t)41,11ttxt)othersx(t)y'(t)2y(t)f(t)(t)(2ee)(t)2ystt13s12H(s)s32s2；；H(z)h(k)）()Tn；T(t)f22(t)(k)(t)為e(2j5)(t)。ft)htd()t_________。0F(j)1。_________。x(k)2。dt243y0ft設(shè)系統(tǒng)的微分方程為，111_________033，t為_________,ft則為。00。H(s)ht。Fjo00Fcosto001f(2tf(t)zH(z)z0.5d2yt)dyt)t)32yt)2ft)h(t)2f(t)e(t)(t)y。p2ppp34圖；(t)(k)(t)(k)為=。1k2。xk與單位樣值序列k。fss2f。。et'。x(k)。Fzz6z2z135。ft)3costt)2t)63sintc412t3y0和。ziH(s)253ssftfc。Xzzzzz是0sgn(t)(k)為f(t)y(t)，則系統(tǒng)無(wú)畸變傳輸?shù)臅r(shí)域表示。4s52s1利用初值定理和終值定