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Unformatted text preview: , place your WATCARD on the table, and ﬁll out the exam attendance sheet
when provided by the proctor after the exam starts.
• Question marks are listed by the question.
• Please, do not separate the pages, and indicate your Student ID at the top of every
page.
• Be neat. Poor presentation will be penalized.
• No questions will be answered during the exam. If there is an ambiguity, state
your assumptions and proceed.
• No student can leave the exam room in the ﬁrst 45 minutes or the last 10
minutes.
• If you ﬁnish before the end of the exam and wish to leave, remain seated and raise
your hand. A proctor will pick up the exam from you, at which point you may leave.
• When the proctors announce the end of the exam, put down your pens/pencils, close
your exam booklet, and remain seated in silence. The proctors will collect the exams,
count them, and then announce you may leave. 1 Problem №1 (25%)
Consider the following zeropole plot of H (z ):
M th order pole (M ≥ 2)
❅ Im(
✻ z) ❅
❅ ❅ ❅
❘
❅M
❤
× −1/2 ❤ Re(z ) ✲ 1/2 Given that H (1) = 3/4 and the the region of convergence (ROC) of H (z ) is z  > 0:
a) Determine H (z ).
b) Determine wether H (z ) is: stable, causal, IIR, FIR, minimumphase, and/or possessing
a generalized linear phase (GLP).
c) Consider the following system
x [n ] ✲ H (z ) x [n ] ✲ ↓2 w[n] ✲ v [n ] ✲ ↓2 G(z ) y [n]✲ r[n]✲ Find G(z ) such that y [n] = r[n]. Problem №2 (25%)
Consider the following two sequences:
x[n] = {−1, −...
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This document was uploaded on 02/28/2014 for the course ECE 413 at University of Waterloo, Waterloo.
 Fall '13
 OlegMichailovich
 Electrical Engineering, Digital Signal Processing, Signal Processing

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