8.1 Representation of Periodic Sequence: the Discrete Fourier Series [小=∑ (2 兀/Nkn xne n AThe sequence x[k] is periodic with period N []=M]]=XN+ [k+N=∑ 2I/Nk+nin n=0 ∑ 1(2xN)。2z xInle n=012 8.1 Representation of Periodic Sequence: the Discrete Fourier Series ◆The sequence is X k  periodic with period N        1 ~ 1 ~ , ~ 0 ~ X = X N X = X N +     ( )( ) 1 0 2 N n j N k N n X k N x n e  − = − + + =    ( )   1 0 2 2 N n j N kn j n x n X k e e   − =   − − = =          ( ) 1 0 2 N n j N kn X k x n e  − = − = 