任意信号通过LTI系统的响应1X(ej?) ejk? dQx[k] :二2元元元1X(ej?)T( ejk?dQy[k] = T(x[k])2元一元元1X(ej?) H(ej?)ejk? dQ2元元Y(ej?)= H(ej?)X(ej?)崔丽珍
崔丽珍 任意信号通过LTI系统的响应 p p p x k X e e d j j k ( ) 2 1 [ ] − = p p p y k T x k X e T e d j j k ( ) { } 2 1 [ ] { [ ]} − = = p p p X e H e e d j j j k ( ) ( ) 2 1 − = (e ) (e ) (e ) j j j Y = H X
般周期信号通过系统的响应ZW-mkX[m]ej2 mk/ NX[m]Wx[k] =NNm=0m=0N-ZX[m]T (eji2 mk/ N ][k]= T{x[k]]Nm=0N-11X[m]H(ei2 ×m/ N)ej2mk/ NZNm=0当N为奇数时，x[k]，h[k]是实序列H(ej)= H*(e-j2)X[m] = X*[N -m](N-1)/22j2元mk/NRe(X[m]H(ej2 m/N)ZX[O]H(y[k]=NNm=1崔丽珍
崔丽珍 一般周期信号通过系统的响应 mk N N m mk N N m X m N X m W N x k j2 / 1 0 1 0 [ ]e 1 ~ [ ] 1 ~ [ ] ~ p − = − − = = = [ ] {e } 1 ~ [ ]} ~ [ ] { ~ j2 / 1 0 mk N N m X m T N y k T x k p − = = = m N mk N N m X m H N j2 / j2 / 1 0 [ ] (e )e 1 ~ p p − = = 当N为奇数时, x[k], h[k]是实序列 *[ ] ~ [ ] ~ X m = X N − m (e ) (e ) j − j H = H [ ] (e )e } ~ Re{ 2 [0] (e ) 1 ~ [ ] ~ j2 / j2 / ( 1)/ 2 1 j0 m N m k N N m X m H N X H N y k p p − = = +