Discrete Fourier series pair 2丌 ◆ The fourier series:n=1∑[k]eN k=0 To obtain the Fourier series coefficients we multiply both sides(2m/ N)rn for0≤n≤N-1 and then sum both the sides we obtain ∑ x(n)en"=∑1∑x(k(krm 2丌 0 =0 k=0 2丌 ∑x(21e (k-r)n n=09 Discrete Fourier Series Pair ◆The Fourier series: 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 − −  = = − =  ◆To obtain the Fourier series coefficients we multiply both sides by for 0nN-1 and then sum both the sides , we obtain j n (2 / ) N r e −  1 1 0 0 2 ( ) ( ) 1 n N k N j n N k r N X k e − −  = = − =    1 0 2 1 [ ] j N N k kn x n e X k N −  = = 