zXnnu nx已知?? 11 1)( 1 0????????? zz znuZ n n 求导两边,对式对 1 1 01 1 ???????? zz z n n21 0 11)1( 1)( ???????? z zn n n两边同时乘以 z -1,可得???? 2 0)1(??????? z zznnnu Z nn1?z同理可得 3 0 2 2)1( )1()(???????? z zzznnun nn4 2 0 3 3)1( )14()(????????? z zzzznnun nn??)(d d)()( 1 1zXz znxnZnxn m m m??????????n是离散变量,所以对 n没有微积分运算; z是连续变量,所以对 z有微积分运算。四.指数序列 1.右边序列)()(nuanx n???????? 0n nnzazXaz z az?????11 1az?,e,e b bza??设当?? b bnz znuZe )(e??则,1,e 0j??za ω设当?? 0 0j je )( ω nωz znueZ??则???? 1 .2????nuanx n 左边序列?? az zzX??az?注意: z 变换相同时,左边序列的定义。?? 1???na n五.正弦与余弦序列单边余弦序列???? nun 0 cos ??? 2 ee cos 00jj0 nωnωnω???因为???? n nωz znuZ 0 0j je e ???1?z???????? 1 cos 2 cos ee 2 1 cos 0 2 0 jj 0 0 0???????????????ωzz ωzzz zz znunωZ nω nω所以同理?????? 1 cos 2 sin ee j2 1 sin 0 2 0 jj 0 0 0??????????????ωzz ωzz zz znunωL nω nω
全文预览
