8. 1 Representation of periodic Sequence: the Discrete Fourier Series X[小]=∑川e j(2T/N) kn CThe sequence X k] is periodic with period N ￥0=X[M,X[=X[N+1 对k+N=∑小]e n=0 ∑划小e|e2=] n=013 8.1 Representation of Periodic Sequence: the Discrete Fourier Series ◆The sequence is X k  periodic with period N X X X X 0 , 1 1  = = + N N          ( ) 1 0 N 2 n j k n N N X k x n N e −  = − + + =      1 0 2 N 2 n j kn N j n x n X k e e  −  = −   − = =          ( ) 1 0 2 N n j N kn X k x n e  − = − = 