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 Jan
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 C
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
ECE 310
University of Illinois at Urbana-Champaign
Spring 2012
Profs. Do & Smaragdis
Homework 5
Due: Friday, Feb. 24th
Problem 1
Determine if the systems characterized by the following relations are,
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 y
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
ECE 310
University
Profs. B resler & Liang
o f I llinois
a t U rbana-Champaign
H omework 2
Reading: C hapter 2 .1-2.6
F all 2 011
D ue: F biday, S eptember
2
Fbr t he s ignal r (t) : e 3t1u1t1- u ,(t
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 I
ECE 310
University of Illinois at Urbana-Champaign
Profs. Bresler & Liang
Homework 3
Reading: Chapter 3
Fall 2012
Due: Friday, September 21
REMINDER: General Instructions for HW
Make sure you write y
University of Illinois at Urbana-Champaign
ECE 310: Digital Signal Processing
PROBLEM SET 1: SOLUTIONS
Problem 1
Solution:
1. (3150 ) + (5 60 ) + (4120 )
= 3cos(150 ) + 5cos(60 ) + 4cos(120 ) + j(3sin
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
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 LS
University of Illinois
Fall 2014
ECE 310: Problem Set 5
Linear and shift invariant systems; Convolution; Impulse response
Due:
Reading:
Wednesday October 1 at 6 p.m.
310 Course Notes Ch 3.33.9
1. [Sys
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 4 Solution
Problem 1
Since = T and T =
1
1000
sec, the signal fr
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]. Ddetermi
I ]NIVtrRSITY O F I LLINOIS A T I JRBANA-CHANcfw_PAIGN
Departrnento f E lcctrical a nclC ontprtterE ngirreerring
S
trCE i i l tt D tc;I'rAL tcNALP IIo(TESSING
Homework 5 S olution
Spring 2 012
Problem
ECE 310
University of Illinois at Urbana-Champaign
Profs. Bresler & Radhakrishnan
Homework 2
Reading: Chapter 2.1-2.6
Fall 2015
Due: Friday, September 11
General Instructions for HW
Make sure you wri
University of Illinois
Fall 2014
ECE 310: Problem Set 7: Problems and Solutions
Convolution via z-transform; Dierence equations; System analysis; BIBO
stability
Due:
Reading:
Version:
Wednesday Octobe
ECE 310
University of Illinois at Urbana-Champaign
Spring 2012
Profs. Do & Smaragdis
Homework 3
Due: Friday, Feb. 11th
Problem 1 Evaluate the following expressions.
a: Find the inverse DFT of the sequ
LP F : Ga () =
T
0
| <
else
T
, ga (t) = sinc
t
T
Xa
= Xd Urbana-Champaign
University ofIllinois at()Ga ()
T
X () = X ( )G ()
a
a
ECE 310: Digital d
Signal Processing
xa (t) = x(nT ) ga (t)
PROBLEM
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
University of Illinois
Fall 2014
ECE 310: Problem Set 8: Problems and Solutions
System Magnitude and Phase; Linear Phase; Filters
Due:
Reading:
Wednesday October 22 at 6 p.m.
310 Course Notes Ch 5.1-5
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 l
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 t
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 w
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]. Ddeterm
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
Homework #10 Solutions
ECE 310 Fall 2017
Problem 1
(10 points) The transfer functions of three LSI systems are given below. For each system, determine if it
is an FIR or an IIR filter (justify your an
University of Illinois
Fall 2017
ECE 310: Problem Set 10
Due: 1pm, November 9, 2017
1. The transfer functions of three LSI systems are given below. For each system, determine if it is an
FIR or an IIR
Homework #6 Solutions
ECE 310 Fall 2017
Problem 1
(25pts) An LSI system is described by the difference equation
y[n] = x[n] + x[n 10]
(10pts) (a) Compute and sketch its magnitude and phase response (1
University of Illinois
Fall 2017
ECE 310: Problem Set 9
Due: 1 pm, November 2, 2017
L
1. Assume that xa (t) =
=1 A cos( t), where the A have positive values. We further assume
that xa (t) is measured
University of Illinois
Fall 2017
ECE 310: Problem Set 12
Due: 1 pm, November 30, 2017
1. (a) Figure 1 shows two magnitude frequency responses. For each of these determine whether
it corresponds to an