Discrete Fourier Series Pair 测=太2[] 27 kn ◆The Fourier series: N k二0 To obtain the Fourier series coefficients,we multiply both sides by e-j(2/N)rn f for0sn≤N-1, and then sum both the sides we obtain e废2ee n=0 -2p4"方k位动e8 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 −  = =  1 0 1 0 2 2 [ 1 ] N k N n j n j nr N N k X k N e e − −   = =   − =      X k 