(word完整版)信号与系统的公式汇总分类,推荐文档

1、1连续傅里叶变换F(j)f(t)ejW1itf(t)F(j)ejtd2连续拉普拉斯变换(单边)stF(s)0f(t)edtf(t)土jJF(s)estds3离散Z变换(单边)F(z)f(k)zkk0.1_k1_f(k)。F(z)zdz,k02jL4离散傅里叶变换F(ej).f(k)ejk1iikf(k)2F(ej)ejd线性afi(t)bf2(t)aFi(j)bF2(j)线性af1(t)bf2(t)aF1(s)bF2(s)线性af1(k)bf2(k)aF1(z)bF2(z)线性af1(k)bf2(k)aF1(ej)bF2(ej)时移f(tto)ejt0F(j)时移f(tt0)est0F(s)时

2、移f(km)zmF(z)(双边)时移f(km)ejmF(ej)频移ejotf(t)F(j(o)频移e琳f(t)F(ss0)频移ej0kf(k)F(ej0z)(尺度变换)频移ejk0f(k)F(ej(0)尺度变换b1j-f(atb)eaF(j-)|a|a尺度变换bf(atb)沽eF)尺度变换akf(k)F(W)a尺度变换f(k/n).f(n)(k)0F(ejn)反转f(t)F(j)反转f(t)F(s)反转f(k)F(z1)(仅限双边)反转f(k)F(ej)时域卷积fi(t)*f2(t)Fi(j)F2(j)时域卷积f(t)*f2(t)F(s)F2(s)时域卷积f1(t)*f2(t)F(z)F2(z

3、)时域卷积f(k)*f2(k)F(ej)F2(ej)频域卷积1fl(t)f2(t)2-F(j)*F2(J)时域微分f(t)sF(s)f(0)2f(t)s2F(s)sy(0)y(0)时域差分f(k1)z1F(z)f(1)f(k2)z2F(z)z1f(1)f(2)f(k1)zF(z)zf(0)2一2f(k2)z2F(z)z2f(0)zf(1)频域卷积f1(k)f2(k)：2自(4)F2(ej()d时域微分f(th'f(n)(t)JF(J)/(J)nF(J)时域差分f(k)f(k1)(1ej)F(ej)频域微分fndF(j)dnF(j)tf(t)“jt)nf(t)j(j7Jd/dnS域微分t

4、f(t),，'(t)nf(t)F(s)/1Z域微分dF(z)kf(k)*频域微分dF(eJ)kf(k)j-d时域积分tF(j)f(x)dx,f()0F(0)()J时域积分tf(x)dx空已虹ss部分求和kzf(k)*(k)f(i)-iz1时域累加F(ej)i0f(k)'/F(ej0)(2k)k1ek频域积分f(0)tF(j)d,F()0(jt)S域积分平F()dtsZ域积分f(k)zmF()dkm-zm1f(0)limF(z),f(1)limzF(z)zf(0)对称F(Jt)2f()初值f(0)limsF(s),F(s)为真分式s初值f(M)limzMF(z)(右边信号)，f(

5、M1)limzM1F(z)zf(M)帕斯瓦尔E|f(t)|2dt2-|F(J)|2d终值f()|im°sF(s),s0在收敛域内终值f()z叫z1)F(右边信号)帕斯瓦尔|f(k)|2:2|F(ej)|2dk2信号与系统公式性质一览表常用连续傅里叶变换、拉普拉斯变换、Z变换对一览表连续傅里叶变换对F(j)f(t)ejtdt拉普拉斯变换对(单边)_stF(s)0f(t)edtZ变换对(单边)F(z)k°f(k)zk函数f(t)傅里叶变换F(j)函数f(t)象函数F(s)函数f(k),k0象函数函数f(k),k0象函数(t)/i1/2()(t)1(k)1(km),m0mz(t)

6、/(t)j/(j)n(t)s1z(km),m0zmzz1(t)1()j(t)1s(k)zz1k2(k)2zz(z1)3t(t)1j()t(t)Rn(t)上/二s2/sn1k(k)z(z1)2(k1)ak(k)二)2et(t)混t(t),01/(j)2e(t)/te“(t)1/1s/(s)2ak(k)zzakak1(k)z(za)2cos(ot)sin(ot)(o)(o)j(o)(o)cos(t)(t)sek(k)zzekak(k)azs22(za)21tjsgn()sin(t)(t)s22ejk(k)zzejk2ak(k)22azaz3(za)|t|22"cosh(t)(t)s22s

7、k,、ka(a)(k)2az22zak,、ka(a)(k)2a二2ejd20)sinh(t)(t)s22耕(k)z(z1)3y(k)(zz；etcos(t)(t)jetcos(t)(t)sokKkabzk1bk12z(j)22(s)22(za)(zb)ab(k)ab(k)(za)(zb)etsin(t)(t)etsin(t)(t)cos(k)(k)z(zcos)sin(k)(k)zsin(j)22(s)222-.z2zcos12-.z2zcos1e”(t),0222(b0tb1)(t)b0b1scos(k)(k)2,、zcoszcos()2-/z2zcos1sin(k)(k)2.，、zsinz

8、sin()27:z2zcos1t,tnj2()/2(j)n(n)()%(电bi)et(t)bsb0akcos(k)(k)z(zacos)aksin(k)(k)azsins(s)2。2z2azcosa2。2z2azcosasgn(t)21tsin(t)(t)1akcosh(k)(k)z(zacosh)aksinh(k)(k)azsinhs2(s22)2-,2z2azcosha2-,2z2azcoshaet,t0et,t0，j_2_J2211t)sin(t)(t)231(s22)2ak(k),k0kIn_zaak(k)k!aecos(一t),|t|一2f(t)0，|t|一2cos()22(成2顼1

9、tsin(t)(t)2s(s22)2j1a至1Wcoshjzi-jntFnen22Fn(n),mnI=sin(t)tcos(t)(t)2s(s22)2己(k)k1zzlnz1(k)2k11 厂Ic*'z1寸zIn2 A1T(t)(tnT)n()(n)n2Ttcos(t)(t)22sb°耳etb0b1tb1sb0,22、2(s)-()e(IJ(s)(s)1,|t|-g(t)0,M7-2.Sasin22(b0b1)tb1etbs虫(s)2,2,2rb0b1b2_t屏b1b2_tb?s2b1sb0e()()岛1b2t()()()()(t)Wsa(Wt)smwitW1,|TF(j)2

10、c，W0,|2Aetsin(t)(t),其中jb0b(j)AAeb1sb0用加b22tb0b1b2之tcete()2b0b1b2(2)t(e(t)b2s2bisbo2(s)2(s)1*|2f(t)0,|t|-2一Sa224b2e“(b12b2)te“122t一(屏加b22)t2e七(t)2b2s2b1sb0/、3(s)0?22etAsin(t)(t)其中Aej(屏bj2)'b2s2lsb022(s)(s22)1-(t2>,|t|20，|t|2jeFSa一2i,|t|42f(t)(1纠，旦|t|-i220,|t|-28.(i).(i)sinsin1-2(i)44b°

11、9;2场2e七Ae七sin(t)(t)()22苴中Aej&b(_j_)2丹甲Ae(j)b2s2b,sb°(s)(s)22)f(t)双边拉普拉斯变换与双边Z变换对一览表双边拉普拉斯变换对_stF(s)f(t)edt双边Z变换对F(z)f(k)zkk函数象函数F(s)和收敛域函数象函数F(z)和收敛域(t)1,整个S平面(k)1，整个Z平面(n)(t)sn,有限S平面n(k)nz(",|z|0(z1)(t)1,Res0s(k)z,|z|1z1t(t)1r，、,Res0s(k1)(k)2,|z|1(z1)tn1-(t)(n1)!1r，、cF,Res0s(kn1)!(k)k

12、!(n1)!nn,|z|1(z1)(t)1-,Res0s(k1),|z|1z1t(t)1r，、c,Res0s(k1)(k1)22,|z|1(z1)tn11r，、.,Res0s(kn1)!(kdnzI-7IA(t)(n1)!k!(n1)!n,|z|1(z1)eat(t)1,ResReasaak(k),|z|a|zateat(t)1、一、2,ResRea(sa)(n1)an(k)22,|z|a|(za)tn1at小1，、,ResRea(sa)(kn1)!n心a(k)k!(n1)!nz|7|a|e(t)(n1)!n,|z|a|(za)eat(t)1,ResReasaka(k1),|z|a|zatn1

13、uat1，、(kn1)!n,小nze(t)(n1)!n,ResRea(sa)a(k1)k!(n1)!n,|z|a|(za)cos(t)(t)s-2,Res0scos(k)(k)2zzcos2-z2zcos1sin(t)(t)22,Res0ssin(k)(k)zsin2z2zcos1e七cos(t)(t)s一一，、22,ResRea(s)akcos(k)(k)2zzacos2-z2zacos1e七sin(t)(t)22,ResRea(s)aksin(k)(k)zasin2z2zacos1et|,Rea)02a22,ReaResReasaa|k|,|a|1(a21)z1,|a|(za)(az1)a

14、eflsgn(t),Rea02s_2s2,ReaResReasaa|k|sgn,|a|1a(z2z),|a|z|1|(za)(az1)a卷积积分一览表""(t)fi()f(t)dfi(t)f2(t)fi(t)*f2(t)f1(t)f2(t)")*f2(t)f(t)(t)f(t)f(t)(t)f(t)f(t)(t)tf()d(t)(t)t(t)et(t)(t)-(1et)(t)(t)t(t)-t2(t)2e1t(t)e2t(t)1+(elte2t)(t),i221et(t)et(t)tet(t)te”(t)e2t(t)Jeite2t(t)(21)(21)21t(t)

15、et(t)t11t22eeltcos(t)(t)e2t(t)C0S(t)e1tC0S()e2t(t)J(21)22&21)22arctan21te“(t)et(t)“2卷积和一览表L(t)*f2(t)f(i)f(ki)f1(t)f2(t)")*f2(t)f1(t)f2(t)f1(t)*f2(t)f(k)(k)f(k)f(k)(k)kf(i)i(k)(k)(k1)(k)k(k)(k)1-(k1)k(k)2ak(k)(k)1ak1(k),a01aaf(k)a(k)k1k1(k),a1a2a1a2ak(k)ak(k)(k1)ak(k)k(k)ak(k)七(k)J(k)1a(1a)2k(k)k(k)1Jk1)k(k1)(k)6akcos(k)(k)ak(k)a*1cos(k1)la；1cos()«>qa2a|qa2cosa1sinarctan!acosa2关丁(t)、(k)函数公式一览表f(t)(t)f(0)(t)f(t)(tto)f(to