8.1 Representation of Periodic Sequence: the Discrete Fourier Series Given a periodic sequence [n]with period N so that [n]=n +rN] The Fourier series representation can be written as (defined as): 网=表∑]e2wm Fourier series representation of continuous-time periodic signals require infinitely many complex exponentials, These complex exponential sequences are periodic g2k+m0n=e8e2m=e/3,k=01,2,N-16 ◆Fourier series representation of continuous-time periodic signals require infinitely many complex exponentials, ◆These complex exponential sequences are periodic : 8.1 Representation of Periodic Sequence: the Discrete Fourier Series ( ) 2 j k N N m n e  + ◆The Fourier series representation can be written as 2 j n N k e  = ( ) 2 2 j n N k j mn e e   = (defined as): (2 / ) ( ) ( ) , j t k T k k x t x t a T e  + =− + = = 1 (2 / ) ( ) jk T t k T T a x t e dt −  = 