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