B is it stable c if the input to the system is 1 x n

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: x[n − 1]) . a) Find the impulse response h[n] of the system. b) Is it stable? c) If the input to the system is ￿ 1, x [n ] = 0, n ≥ 0 & n is even otherwise what is the output y [n] of the system? Recall: −1 • Z{u[n]} = (1 − z −1 ) , |z | > 1. −1 • Z{an u[n]} = (1 − a z −1 ) , |z | > |a|. • Partial fraction expansion: Ak = (1 − dk z −1 )X (z )|z=dk . Question 2 [35%]: A continuous time signal xc (t) has the following Fourier transform: Figure 1: Pertaining to Q-2 a) What is the Nyquist rate corresponding to the signal? 2 b) What is the lowest sampling frequency which can be applied to xc (t) without causing aliasing distortion? Draw the DTFT of x[n] in this case. c) Draw the block-diagram of the reconstruction system that will recover xc (t) from the sampled signal x[n] if the sampling rate is set to its lowest possible value. Sketch the frequency response (i.e. Fourier transform) of the reconstruction filter that is used in this case. Question 3 [30%]: Consider the following two systems: Figure 2: Pertaining to Q-3 Write Y1 (z ) and Y2 (z ) as a function of X (z ). Are Y1 (z ) and Y2 (z ) equal? 3 University of Waterloo Department of Electrical and Computer Engineering ECE 413 – Digital Signal Processing Final Exam, Spring 2009 August 13, 2009, 9:00-11:30 AM Instructor: Dr. Oleg Michailovich Student’s name: Student’s ID #: Instructions: • This exam has 4 pages. • No books and lecture notes are allowed on the exam. Please, turn off your cell phones, PDAs, etc., and place your bags, backpacks, books, and notes under the table or at the front of the room. • Please...
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