《完整版信号与系统的公式汇总分类》由会员分享，可在线阅读，更多相关《完整版信号与系统的公式汇总分类（8页珍藏版）》请在金锄头文库上搜索。
1、1连续傅里叶变换2连续拉普拉斯变换（单边）3离散Z变换（单边）4离散傅里叶变换F（ej ）f（k）e jkkF(j )f(t)e j tdtF(s)f(t)0 f(t)e1j2 j jstdtstF (s)e dsF(z)f(k)f(k)z kk 021j：F(Z)Zk 1dz,k 0f(t) + F(j )ej td1f(k) 2 F(ej )ej kd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)aFdz) bF2(z)线性af1(k) bf2( k)aF1(ej ) bF2(ej )时移f (
2、t to)e j *F(j )时移f (tt)e st0F (s)时移f(k m) z mF（z）（双边）时移f (k m)e j mF(ej )频移e j otf (t)F(j(o)频移e st f (t)F (s s0 )频移e j0k f(k)F(e j0z）（尺度变换）频移e jk 0 f (k)F(ej(0)尺度b1 ja e a尺度bsF(f)尺度F(j尺度f(k/ n)-)F(ejn )变换f(at b)F(j-)变换f (at b)变换akf (k)变换f(n)(k)0|a |a|aa反转f( t)F( j)反转f( t)F( s)反转f( k) F(z 1)（仅限双边）反转f
3、( k)F(e j )时域时域时域时域h(ej )F2(ej )卷积fi(t)* f2 (t)Fi(j)F2(j )卷积f1(t)* f2(t)h(s)F2(s)卷积f1(t)* f2(t)F1(z)F2(z)卷积f1(k)* f2(k)频域fi(t)f2(t)j)*F2(j )f (k1) z 1F(z)f( 1)频域1f1(k)f2(k)亍 2)F2(ej()d卷积时域f(t) sF(s)f(0 )时域f (k2) z 2F(z)z 1f ( 1) f ( 2)卷积时域f卄微分f(t)s2F(s)sy(0 ) y(0 )差分f (k1)zF(z) zf(0)时域(1 ej )F(ej )微
4、分j F(j )/(j )nF(j)f (k22) z F (z)2z f(0) zf (1)差分f(k) f(k 1)频域tf(t)( jt)n f(t).dF(j j )/dnF(j)S域+n f/ dn F (s) fyZ域kf(k)dF(z) z频域kf (k).dF(ej )/nJ微分d/d n微分dsn微分dz微分d时域tf (x)dx, f ()0 F( jj )F(0)()时域tf(x)dxF(s)f(1)(0)部分kf(k)* (k)zf (i)_:时域F(ej ) f(k) j 丿k1 ejF(ej0)(2 k)积分积分ss1求和iz 1累加k频域f (0)t 旦氏F(j)
5、d ,F()0S域f(t)F( )dZ域f (k)zmF( )df(0) lim F(z) , f(1)lim zF(z) zf (0)积分(jt)积分ts积分k mzm 1z，z对称F(jt)2 f()初值f (0 ) lim sF (s), F (s)为真分式 s初值f(M)lim zM F（z）（右边信号），zf (M 1) lim zM 1 F(z) zf(M )z帕斯E|f(t)|2dt丄|F(j )|2d终值f()lim sF(s),s 0在收敛域内终值f()lim(z 1)F (z)(右边信号)帕斯2|f(k) |2 -1|F(ej )|2d瓦尔2瓦尔k2信号与系统公式性质一览表
6、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拉普拉斯变换对(单边)Z变换对(单边)F(j )f (t)e j tdtF(s) o f(t)estdtF(z)kf(k)zk0函数f(t)傅里叶变换F(j )函数f(t)象函数F(s)函数f(k),k o象函数函数f(k),k 0象函数(t) /11/2 ()(t)1(k)1(k m), m 0z m(t)/ (n)(t)j /(j )n(t)s1z(k m), m 0zm zz 1(t)1()j(t)1(k)zk2 (k)z2zsz 1(z 1)3t (t)1j ( ) -rt (t)ftn (t)1 in! s2 / sn
7、1k (k)z(k 1)ak (k)z2(z 1)2(z a)2e t (t) /tet (t),01 / 1e 七(t)/te t (t)ak (k)zkak 1 (k)zj /( j )2s / (s )2z a(z a)2cos( ot)(o)(o)cos( t) (t)se k (k)zkak (k)azsin( ot)j (o)(o)s22z e(z a)21j sgn()sin( t) (t)ej k (k)zaz2 a2zts22z ejk a (k)(z a)|t|2cosh( t) (t)sak ( a)kzkka ( a)“.、z22s222a(k)2 2 z a2a(k)
8、z2 a2J2(o)sinh( t) (t)k(k 1) (k)z(k 1)k (k)z2e j 0s222 (k)(z 1)32 (k)(z 1)3jsak bkzk 1, k 1ab八z2e t cos( t) (t)(j)22e t cos( t) (t)(s )22a b (k)(z a)(z b)H (k) a b(z a)(z b)e tsin( t) (t)e t sin( t) (t)cos( k) (k)z(z cos )sin( k) (k)zsin(j)22(s )222z 2zcos12z 2zcos1Q |t| o22 2(b0tb1)bos2b scos( k )
9、(k)z2 coszcos()sin( k)(k)z2 sinzsin()z22zcos12z 2z cos1t护j2()/2 (j)n(n)()b0 (b0b1)e t (t)4 sb)akcos( k) (k)z(za cos )ak sin(k)(k)az sins(s)2 z22azcosaz2 az cosasgn(t)2tsin( t) (t)1ak cosh( k) (k)z(za cosh )ak sinh(k)(k)az sinh厂s2(s22)2 z22azcosha2 一- 2 z2az coshae t ,t 0t,(t,t 00).2j 2 2丄12 3t) sin(
10、 t) (t)1aklnzak(k)ae(s22)2j(k), k0kz a帀ecos(t),|t| 一cos(丄ts2s(ln a)k (k)11f (t)22n( t) (t)门cosh z0,|t| 22 (R匕-)2(s22)2k!(k)a z(2 k)!Fnejnt2Fn ( n ),21sin( t)tcos( t) (t)2 s(k)zlnz1(k)LgjG 1(s22)2z 1nnT2k 12k 12Jz 1nT)() (n)s22bobitbo b1t.bqSboT(t)(tnntcos( t) (t)re(e(t)2(s22)2匸(严(s)(s)T1,|t|rb0b1b2 2 tbob1b2 2e t2o2.(b。S)tbje七6sb) e( )( )()()b2s2bSbog(t)Sasin2(s、2心 Eb2 2 e
