8.1 Representation of Periodic Sequence: the Discrete Fourier Series 区]=∑对e 2/N)k 7=0 OThe sequence x[k] is periodic with period N x[]=X[M,x[=x[N+ X[+M=∑F[]e 兀(k+Nn n=0 kn ∑ xInle e/zn=Xkk n=012 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  − = − = 