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Revision as of 15:51, 1 February 2019
Communicates & Signal Process (CS)
Question 2: Signal Processing
August 2017
Problem 1. [50 pts]
Equation 1 below is the formula for reconstructing the DTFT, $ X(\omega) $, from $ N $ equi-spaced samples of the DTFT over $ 0 \leq \omega \leq 2\pi $. $ X_{N}(k) = X(\frac{2\pi k}{N},k=0,1,...,N-1) $ is the N-pt DFT of x[n], which corresponds to N equi-spaced samples of the DTFT of x[n] over $ 0 \leq \omega \leq 2\pi $.
(a) Let x[n] be a discrete-time rectangular pulse of length $ L=12 $ as defined below:
(i) $ X_{N}(k) $ is computed as a 16-point DFT of x[n] and used in Eqn (1) with N=16. Write a close-form expression for resulting reconstructed spectrum $ X_{r}(\omega) $.
(ii)
