Discrete Fourier Series Pair k-r)n 1,k-r=mN,mis an integer 10,otherwise Using orthogonality of the complex exponentials: =]=[k灯 n=0 k=0 0≤r,k≤W-1 0only when k-r=0 (m=0,k=r) Xk-岁ae n=0 D5之a coefficients The Discrete Fourier Series Periodic 10 0 only when k − =r 0 10 Discrete Fourier Series Pair 1 0 2 1 ( ) N n j k r n N N e −  = −  = = X X [ ] [ ] r k 1 0 2 [ ] N n j n N r x n e −  = −  0 1 1 0 2 ( ) [ ] 1 N n N k j k r n N N X k e − −  = = − =   1, - , 0, k mN mis aninteger othe e r rwis = =   (2 ) 1 / 0 1 [ ] j N N k kn x n e X N k  − = =  1 0 2 [ ] N n j n N k x n e −  = − X[ ] k =  The Discrete Fourier Series coefficients Periodic Using orthogonality of the complex exponentials: DFS 0 1   − r k, N ( 0, ) m k = = r