Solved: Let x[n] be a periodic sequence with period N and Fourier series representation
Chapter 3, Problem 3.49(choose chapter or problem)
Let x[n] be a periodic sequence with period N and Fourier series representation x[n] = L akejk(27TIN)n. k= (P3.49-1) (a) Suppose that N is even and that x[n] in eq. (P3.49-1) satisfies x[n] = - x [ n + ~] for all n. Show that ak = 0 for all even integers k. (b) Suppose that N is divisible by 4. Show that if x[n] = -x[n +~]for all n, then ak = 0 for every value of k that is a multiple of 4. (c) More generally, suppose that N is divisible by an integer M. Show that if (N/M)-1 [ N] ~ x n + r M = 0 for all n, then ak = 0 for every value of k that is a multiple of M.
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