2 c find q n whose dft is given by qk w k 2 mod

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3, −1, 5}, w[n] = {0, 7, 0, 5}. a) Determine if a sequence that satisfies x ￿ y = w can be found. If so, find y [n]. If not, prove it does not exist. b) Given that W [k ] = DFT4 {w[n]} = Im{G[k ]}, find g [3] − g [1]. 2 c) Find q [n] whose DFT is given by: Q[k ] = W [(k − 2) mod 4] W4 k . 2 Problem №3 (15%) A DFT engineer would like to use windowing and zero padding to analyze the DFT of a sampled signal. a) Given that the signal was sampled using a sampling frequency of 128 Hz, and that the engineer intends to use a rectangular window and apply the DFT of length N = 64 to the signal, what is the minimal distance (in Hz) between two distinguishable frequency components of the signal? b) Which of the following two is the proper procedure: • Zero-pad, multiply by a window, apply FFT; • Multiply by a window, zero-pad, apply DFT. Problem №4 (25%) In STFT analysis, the DTFT is applied to windowed versions of a sequence x[n], namely X [n, λ) = DTFT{x[m + n] w[m]} = ∞ ￿ x[n + m]w[m]e−λm . m=−∞ Alternatively, one can apply the DTFT to the auto-correlation sequence a[n] of the windowed signal x[m + n] w[m] which is defined as: a[m, n] = ∞ ￿ x[n + l] w[l] x[n + m + l] w[m + l]. l=−∞ Find the DTFT A[n, λ) of a[m, n] in terms of X [n, λ). (Assume real sequence and window.) Problem №5 (10%) ω | ✻H (e )| 1 ❈ ❈ ￿ ❈ ❈ ❈ ❈ ❈ ❈ ❈ ❈ ❈❈ ω π 3 ✲ Considering the above response of an FIR generalized linear phase (GLP) filter, which of the following statements is correct: a) The filter is Type I; b) The filter is Type II; c) The filter is Type III; d) The filter type cannot be determined from the graph. Explain your answer. 4...
View Full Document

This document was uploaded on 02/28/2014 for the course ECE 413 at University of Waterloo, Waterloo.

Ask a homework question - tutors are online