8.1 Representation of Periodic Sequence: the Discrete Fourier Series +a periodic sequence x[n] with period N, [n=x[n+rN for any integer The discrete Fourier series: 2丌 Synthesis equation k=0 ◆ Coefficients: N-1 2丌 j<-kn Analysis X(k)=∑(n)e equation 1 011 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: