《信号与系统》课程教学课件（PPT讲稿）时移加尺度变换证明

时移加尺度变换证明 F(@)=[f(at+b)e-i dt 当a>0时，设t+b=x,则t=x-b,dt=1dx -x) 当时4设=则=。号 ,dt=- -jox-b -jxj e-ior==e F(@)="f (x)e x=

X 第 1 页 jh jh 时移加尺度变换证明 ( )   − − F = f at + b t t ( )e d j 1   ( )   − − =   x a F f x a b x a d 1 ( )e e j j 1    a b a F a  j e 1       = a b x a a x b t     j j j j e = e = e  e − − − − ( )  −  − − =   x a F f x a b x a d 1 ( )e e j j 1      − − = f x  x a a b x a ( )e e d 1 j j  a b x a a b a F a f x x a   j j  j e 1 e ( )e d 1       = =   − − x a t a x b a at b x t d 1 0 , , ,d = − 当  时 设 + = 则 = x a t a x b a x b a a a at b x t d 1 0 , , , ,d = − − − = − 当  时 = − 设 + = 则 =