Discrete fourier series pair 2兀 n ∑x n) N ∑)1c解k n=0 k=0 n=0 N 2丌 (k-r)n k-r=mN, m an integer ∑ 0. otherwise Problem 8.51 HW (n) X(r) n=0 2丌 (k)=∑(m)eN n=0 对小=∑[ke k=09 Discrete Fourier Series Pair 1 0 2 ( ) 1, - , 0, 1 N n j k r n N k r mN m an integer N otherwi es e −  = −  = =    1 0 2 ( ) ( ) N n j N r n x n X e r −  = −  = 1 0 2 ( ) ( ) N n j kn X k x n N e −  = − =   1 0 2 1 [ ] N k j kn N x n X k N e −  = =  Problem 8.51, HW 1 1 0 0 1 0 2 ( ) 2 1 ( ) ( ) N N n k N n j r j k r n N n N x n X k N e e − −   = = − = − −  = 