XY(k)=∑x(n)W+∑x(n)W n=0(n为偶数)n2=0(n为奇数) X无法显示该图片 =∑x(2n)W+∑x(2r+1)W+k r=0 =∑x()W)+W∑x2()2) r=0 0 由子:WN=e j2/() W 所以,上式可表示为 )∑xW+F∑xW=x1()+Wx2(k 0由于: 所以,上式可表示为:       − = − = − = + − = − = − = = + = + + = + 1 0 2 2 1 0 2 1 1 0 (2 1) 1 0 2 1 0 1 0 2 2 2 2 ( )( ) ( )( ) (2 ) (2 1) ( ) ( ) ( ) N N N N r r k N k N r r k N r r k N r r k N N n N n n k N n k N x r W W x r W x r W x r W X k x n W x n W (n为偶数) (n为奇数) 2 2 2 2 2 2 / ( ) N N W e N e W j j N = = = −  −   ( ) ( ) ( ) ( ) ( ) 1 2 1 0 2 1 0 1 2 2 2 2 X k x r W W x r W X k W X k k N r k r k N r r k N N N = N +  = + − = − =