8.1 Representation of Periodic Sequence:the Discrete Fourier Series X[]=∑[n]e2xa n=0 The sequence]is periodic with period N [o]=[],[]=[N+] k+N-立远ee n=( n=0 经e如eP和-[个 = 1712 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  − = − =    1 0 N 2 2 n j k n n j N N N x n e e −   = − − = 