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/Nk 小=∑[k]e Q Fourier series representation of continuous-time periodic signals require infinitely many complex exponentials, for discrete-time periodic signals 2丌 2丌 k+mN)n j (2rmn k=0.1.2.….N-16 ◆Fourier series representation of continuous-time periodic signals require infinitely many complex exponentials, ◆for discrete-time periodic signals: 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 j k N N m n e  + ◆The Fourier series representation can be written as , 0,1,2, , 1 k N = − 2 j kn N e  = ( ) 2 2 j kn N j mn e e   =