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
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 - 4 ), d etermine t he c ontinuous-timeF ourier t ra'sf
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
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, with respect to the input,
(i) linear or nonlinear (ii)
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
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 your full name and section on your HW solution.
All pag
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 frequency could be
0 =
or possibly
0 =
(
4
1000 = 250
4
)
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
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
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 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. [System properties]
Determine if the systems characterized
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 October 15 at 6 p.m.
310 Course Notes Ch 4.5 Ch 4.10-4.14
1.0
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 sequence X [k ] = cfw_1, ej/2 , 0, ej/2 , where the rst ent
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
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
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
1
(r.) ' !Jl'rl y [" - 3 ] * r ;ln]* 5 .r - 2 l
ln
i)
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 5.1-5.2
1. [Filtering]
The signals below are passed through
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
Profs. Bresler & Radhakrishnan
Homework 2
Reading: Chapter 2.1-2.6
Fall 2015
Due: Friday, September 11
General Instructions for HW
Make sure you write your full name and section on your HW solution.
All
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 SET 5: SOLUTIONS
(t nT )
xa (t) =
x[n]sinc
T
n=
Proble
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
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
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
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.
A
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
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
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 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]
University of Illinois Spring 2017
ECE 310: Problem Set 9
Due: 5pm, March 29, 2017
1. A speech signal $a(t) is assumed to be bandlimited to 12kHz. It is desired to lter this signal with a
bandpass lter that will pass the frequencies between 300Hz and 6kHz
University of Illinois Spring 2017
ECE 310: Problem Set 3
Due: 5pm, February 8, 2017
Reading: 310 Course Notes Chapter 2.5, 2.6
1. Assume ac[n] is a nite-duration sequence of length 40, and y[n] is obtained by zero-padding :c[n] to
length 64. That is, y[n
University of Illinois Spring 2017
ECE 310: Problem Set 6
Due: 5pm, March 1, 2017
1. Compute the convolution y[n] = ac[n] * h[n] for a;[n] and h[n] given below by: a) directly evaluating
the convolution sum, and b) using the ztransform. Give the ROCs for
University of Illinois
ECE 310: Problem Set 8
Due: 5pm, March 15, 2017
1. An LSI system is described by the difference equation
yln] = 33[n] + wln 10]
(a) Compute and sketch its magnitude and phase response
(b) Determine its output to inputs
i. ac[n] = co
University of Illinois Spring 2017
ECE 310: Problem Set 13
Due: 5pm, April 26, 2017
1. Consider the system shown below.
(a) Let :1:[n] = n(u[n] u[n 5]). Determine and sketch y[n].
(b) Let Xd(w) be as shown in the gure below. Determine and sketch Yd(w).
Xd