Name: Math 4564 Homework 9 1. Compute the discrete Fourier transform for each of the sequences below (see the formula provided below). Determine which of the sequences has the Fourier transform that correctly represents the spectrum of the underlying process. N 1 f (j ) = fk e i 2jk N , j = 0, 1, . . . , N 1 k=0 You are allowed (and encouraged) to use calculators or computers to compute the transforms. (a) fk = cos k , k = 0, 1, 2, 3, 4, 5 3 (b) gk = cos 4k , k = 0, 1, 2, 3, 4, 5 5 (c) hk = cos 8k , k = 0, 1, 2, 3, 4, 5 5