8.1 Representation of Periodic Sequence the discrete fourier series Given a periodic sequence x[n] with period n so that 义]=Xn+rN The Fourier series representation can be written as 2丌/N|n 刘=∑平[e k Fourier series representation of continuous-time periodic signals require infinitely many complex exponentials Not that for discrete-time periodic signals since 2丌 2丌 2丌 k+mN)n (2zm) k=0.1.2…,N-16 ◆Fourier series representation of continuous-time periodic signals require infinitely many complex exponentials ◆Not that for discrete-time periodic signals, since 8.1 Representation of Periodic Sequence: the Discrete Fourier Series ◆Given a periodic sequence with period N so that x[n] ~ x[n rN] ~ x[n] ~ = +   1 (2 / ) [ ] k j N kn x n X k N e  =  ( ) ( ) 2 2 2 2 j k n j kn j kn N mN N N j mn e e e e     + = = ◆The Fourier series representation can be written as , 0,1,2, , 1 k N = −