Consider a finite duration sequence x n of length p such that x n 0 for n 0 and n P We want to compute samples of the Fourier transform at the N equally spaced frequencies k 2k N, k 0, 1,, N 1 Determine and justify procedures for computing the N samples of the Fourier transform using only one N point DFT for the following two cases (a) N P (b) N P

Question: Consider a finite-duration sequence x[n] of length p such that x[n] = 0 for n < 0 and n P. We want to compute

Consider a finite-duration sequence x[n] of length p such that x[n] = 0 for n < 0 and n ≥ P. We want to compute samples of the Fourier transform at the N equally spaced frequencies

ωk = 2πk/N, k = 0, 1,…, N – 1.

Determine and justify procedures for computing the N samples of the Fourier transform using only one N-point DFT for the following two cases:

(a) N > P.

(b) N < P

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