8.1 Representation of Periodic equence: the Discrete Fourier Series a periodic sequence x[] with period N, [n]=x[n+rN] for any integer The Discrete Fourier series: =1 2丌 kn ∑X[k]e Synthesis equation k=0 ◆ Coefficients: 2丌 X()= Analysis r(n)eN equation n=0 1212 8.1 Representation of Periodic Sequence: the Discrete Fourier Series ◆a periodic sequence x n  with period N, x n x n rN for any integer r   = +   ◆The Discrete Fourier Series: 1 0 2 ( ) ( ) , N n j kn X k x n N e −  = − =   1 0 2 1 [ ] , N k j kn N x n X k N e −  = =  Synthesis equation Analysis equation ◆Coefficients: