AIR INSTITUTE OF ARTIFICIAL INTELLIGENCE AND ROBOTICS, XJTU 986 证明 y(n)=IDFSX,(KX,k] ∑X1(k)X2(kK k=0 代入:x(k)=∑x1(m)K mk n2=0 N-1N-1 y(n) ∑x(m)X2(k)Wx(n=m)k k=0n=0 ∑x(m) X2(k)入 n-n ∑x(m)2(n-m) n=0 数字信号处理简明教程Institute of Artificial Intelligence and Robotics, XJTU 1986 数字信号处理简明教程 证明： 1 1 ( ) 1 2 0 0 1 1 ( ) 1 2 0 0 1 1 2 0 1 ( ) ( ) ( ) 1 ( ) ( ) ( ) ( ) N N n m k N k m N N n m k N m k N m y n x m X k W N x m X k W N x m x n m − − − − = = − − − − = = − = =   =     = −      1 2 1 1 2 0 ( ) [ ( ) )] 1 ( ) ( ) N kn N k y n IDFS X k X k X k X k W N − − = = =  （ 代入： 则： 1 1 1 0 ( ) ( ) N mk N m X k x m W − = = 