University of Illinois
Fall 2014
ECE 310: Problem Set 4
Sampling, Ideal A/D converter, Aliasing, Analog frequency response of a
digital system
Due:
Reading:
Wednesday September 24 at 6 p.m.
310 Course Notes Ch 3.1, 3.2, 5.3
1. [Sampling and Aliasing]
A co
1
University of Illinois
Summer 2015
ECE 310: Problem Set 1 SOLUTIONS
Due: 8:30 am, June 23, 2015
Reading: 310 Course Notes Chp. 1, Chp. 2.1-2.5, Appendix A, Appendix D
1. Evaluate and represent your nal answer in both Cartesian and polar forms. Try to si
1. Let X[k] be the N-point DFT of the sequence x[n]. Ddetermine the N-point DFT of the
sequence x1 [n] = x[n]cos( 2kn ) 0 n N 1 in terms of X[k].
N
SOLU T ION
j 2 k0 n
j 2 k0 n
k
x1 [n] = x[n]cos( 2N0 n ) = x[n]( 1 e N + 1 e N ). By the circular time shif
University of Illinois at Urbana-Champaign
Department of Electrical and Computer Engineering
ECE 310: Digital Signal Processing I
Problem Set 5
Summer 2012
Reading: Chapter 8: Frequency response of LSI systems, Chapter 9: A/D and D/A
Converters
Problem 1
University of Illinois
Fall 2014
ECE 310: Problem Set 1: Problems and Solutions
DSP overview, Continuous-time (CT) and discrete-time (DT) signals,
Complex numbers, Impulses
Due:
Reading:
Wednesday January 29 at 6 p.m.
310 Course Notes Ch 1, Appendix A, Ap
ECE 310
University of Illinois at Urbana-Champaign
Fall 2011
Profs. Bresler & Liang
Homework 1
Due: Friday, August 26
Reading: Chapter 1 and Appendices A and D
General Instructions for HW
Make sure you write your full name and section on your HW solution
University of Illinois
Fall 2014
ECE 310: Problem Set 2
Discrete-time Fourier transform (DTFT)
Due:
Reading:
Wednesday September 10 at 6 p.m.
310 Course Notes Ch 2.1-2.5
1. [DTFT]
Compute the DTFT of the following sequences. Plot the magnitude and phase o
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 11 Solution
Prof. Bresler, Prof. Liang
Friday, November 16, 2012
Problem 1
Design a length-32 FIR high-pass lter with c
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 5
Profs. Singer & Smaragdis
Spring 2013
Problem 1
Determine if the systems characterized by the following input (x)-out
ECE 310
University of Illinois at Urbana-Champaign
Profs. Bresler & Liang
Homework 2
Reading: Chapter 3
Fall 2011
Due: Friday, September 9
1. Let X[k] be the N-point DFT of the sequence x[n]. Ddetermine the N-point DFT of the
sequence x1 [n] = x[n]cos( 2k
University of Illinois
Summer 2015
ECE 310: Homework 1
Due: 8:30 am, June 23, 2015
Reading: 310 Course Notes Chp. 1, Chp. 2.1-2.5, Appendix A, Appendix D
1. Evaluate and represent your nal answer in both Cartesian and polar forms. Try to simplify
your ans
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Profs. Singer & Smaragdis
Homework 11
Problem 1
1
Design a low-pass FIR lter with cut-o frequency c = 4 and N = 51 points. Use t
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 5
Profs. Bresler & Liang
Due: Friday, September 23, 2011
Problem 1
The continuous-time signal xa (t) has the continuous
University of Illinois
Summer 2015
ECE 310: Homework 2
Due: 8:30 am, July 1, 2015
Reading: 310 Course Notes Sections 2.6, 3.1, 3.2
1. Evaluate the following expressions:
(a) Find the inverse DFT of the sequence X[m] = 1, ej 2 , 0, ej 2
X[m] corresponds to
University of Illinois
Summer 2015
ECE 310: Homework 5
Due: Tuesday, 8:30 am, July 21, 2015
Reading: 310 Course Notes Chp. 5.3, Chp. 6
Figure 1: System diagram for discrete-time processing of continous-time signals.
1. A signal xa (t) is assumed to be ban
ECE 310
University of Illinois at Urbana-Champaign
Profs. Bresler & Liang
Homework 2
Reading: Chapter 2.1-2.6
Fall 2012
Due: Friday, September 14
REMINDER: General Instructions for HW
Make sure you write your full name and section on your HW solution.
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Homework 5 S olution
Spring 2 012
Problem
1
(r.) ' !Jl'rl y [" - 3 ] * r ;ln]* 5 .r - 2 l
ln
i)
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 8 Solution
Prof. Bresler, Prof. Liang
Friday, October 14, 2011
z 7
, causal
z 2 +1/9
1
(|z | > 3 ) contains the unit ci
University of Illinois
Fall 2014
ECE 310: Problem Set 5: Problems and Solutions
Linear and shift invariant systems; Convolution; Impulse response
Due:
Reading:
Version:
Wednesday February 26 at 6 p.m.
310 Course Notes Ch 3.33.9
1.2
1. [System properties]
ECE 310
University of Illinois at Urbana-Champaign
Profs. Bresler & Liang
Homework 3
Reading: Chapter 3
Fall 2011
Due: Monday, September 12
1. Let X[k] be the N-point DFT of the sequence x[n]. Ddetermine the N-point DFT of the
sequence x1 [n] = x[n]cos( 2
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 8
Profs. Bresler & Liang
Due: Friday, October 14, 2011
Problem 1
Determine whether each of the following represents a B
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 13
Profs. Bresler & Liang
Due: Monday, November 28, 2011
Problem 1
Given an input x[n], let v [n] be the output of a sa
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 5 - Solutions
Profs. Singer & Smaragdis
Spring 2013
Problem 1
a) y 2 [n 1] + 2y[n] = x[n]
Nonlinear, causal, shift-inva
University of Illinois
Fall 2014
ECE 310: Problem Set 1
DSP overview, Continuous-time (CT) and discrete-time (DT) signals,
Complex numbers, Impulses
Due:
Reading:
Wednesday September 3 at 6 p.m.
310 Course Notes Ch 1, Appendix A, Appendix D
1. [Complex Va
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 410 Digital Signal Processing
Quiz 1
Professors Shanbhag and Singer
Wednesday Feburary 2nd, 2011
Name:
Section: Morning or Afternoon
Instructions
You may not
ECE 310
University of Illinois at Urbana-Champaign
Spring 2013
Profs. Singer & Smaragdis
Homework 2
Reading: Chapter 2.1-2.6
1. Let x[n] be a signal with DTFT as shown in the following gure. Determine and sketch the
DTFT of y[n] = x[n] cos(n/4).
2. Let x[
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 13
Friday, April 24, 2015
Prof. Liang, Dr. Ravishankar
Due: Wednesday, April 29, 2015
1. Consider the system shown belo
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 9
Dr. Ravishankar & Prof. Liang
Due: Friday, April 3, 2015
Figure 1: System for discrete-time processing of continuous
ECE 310
University of Illinois at Urbana-Champaign
Fall 2015
Profs. Bresler & Radhakrishnan
Homework 1
Due: Friday, September 4
Reading: Chapter 1 and Appendices A and D, Chapter 2 (2.1-2.5)
General Instructions for HW
Make sure you write your full name
ECE 310 Name (please print): 13%;
Fall 2016
Quiz 3 NetID (please print):
10/05/2010
Time Limit: 60 Minutes Section:
This exam contains 5 pages (including this cover page) and 4 questions.
Total of points is 100.
Grade Table (for teacher use only)
25
100
ECE 310 Name: %
Fall 2016
Quiz 1 Netid:
9/7/2016
Time Limit: 60 Minutes
This exam contains 5 pages (including this cover page) and 4 questions.
Total of points is 100.
Rest of instruction.
Grade Table (for teacher use only) ita-Vl'h 5b
ECE 310 Quiz 1 -
ECE 310 Name (please print): _%
Fall 2016
Quiz 2 NetID (please print):_
9/21/2016
Time Limit: 60 Minutes Section:
This exam contains 6 pages (including this cover page) and 5 questions.
Total of points is 100.
Grade Table (for teacher use only) D; Vlr'
UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 DIGITAL SIGNAL PROCESSING
Quiz 4
Professors Bresler and Levinson Wednesday October 19, 2016
Name: Ire, SectionzG (10:00 - 10:50 AM) or E (3:00 3:50 PM)
I