证明 设y(n)=x(n)*x2(m)则 Y()=X1(=)·X2( (e)=X1(e/)·X2(e) X,(elo)x2(e/o)e/onc ∴x1(n) XI(e ) e 2丌 1【2X2( jo cOndo Y(eoe/ndo 2丌 y(n O 2丌 x1(n)*x2(n) x2 X,(e do 2丌 X(e)x2(e/ ) do 丌 =x1(m)*x2(n)l=0 o, (e)x2(el o )do x(k)(n-k X(e)do i ∫x O 2丌 2丌 x(O)·()电磁波信息科学重点实验室视里大学 FUDAN UNIVERSITY证明: −   =  =  =            X e X e e d Y e X e X e Y z X z X z y n x n x n j j j n j j j ( ) ( ) 2 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 1 2 1 2 设 1 2 则 ( ) ( ) ( ) ( ) 2 1 1 2 x n x n y n Y e e d j j n =  = = −       (0) (0) ( ) ( ) ( ) ( )| ( ) ( ) 2 1 1 2 0 0 1 2 1 2 0 1 2 x x x k x n k x n x n X e X e d n n k n j j =        = − =   = = = −           − − = = • • •             x n X e e d x n X e e d j j n j j n ( ) 2 1 ( ) ( ) 2 1 ( ) 2 2 1 1 ∴ − =      x X e d j ( ) 2 1 (0) 1 1 − =      x X e d j ( ) 2 1 (0) 2 2    − − − =                  ( ) } 2 1 ( ) }{ 2 1 { ( ) ( ) 2 1 1 2 1 2 X e d X e d X e X e d j j j j