Ex.8.1 determine the DFS of a impulse train Consider the periodic impulse train -之-则-6wm N points -N-N+1·-2-101 2·N-1NN+1N+2 Solution:X[附-∑sm%==for all k W-e彩 n 大名刚县*=大艺 orthogonality 1414 Ex. 8.1 determine the DFS of a impulse train ◆Consider the periodic impulse train     1, , 0, r n rN r is any integer x n n rN otherwise   =−  = = − =    n -N -N+1…… -2 -1 0 1 2 …… N-1 N N+1 N+2 …… N points xn ~ 1     1 0 0 1 , N kn N n N X k nW W  for all k − = Solution: = = =      1 0 1 N kn N k x n X k W N − − = =  0 1 2 1 N j k N n k e N −  = =  orthogonality 2 N j W e N  − = 1 0 1 N kn N k W N − − = = 