Discrete Fourier Series (DFS) []=∑n]e ◆Let Wv=e N ◆Analysis equation:[k]=∑[nW n=0 ◆Synthesis equation:]-=∑[m 三0 like CFS periodic discrete diserete periodicnk periodic discrete discrete like DTFT periodic 1313 Discrete Fourier Series (DFS) ◆Let 2 N j W N e  − =     1 0 N kn N n X k x n W − = =      DFS x n X k  ◆Analysis equation:     1 0 1 N kn N k x n X k W N − − = ◆Synthesis equation: =      1 0 N 2 n j kn N X k x n e −  = − =  periodic discrete like CFS discrete like DTFT periodic discrete periodic periodic discrete (2 / ) ( ) ( ) , j t k k T k x t x t a e T  + =− + = =