Hd (!)
Hd (!) = |Hd (!)|ei\Hd (!)
!
\Hd (!) = 0
!c
h(n) = (n)
h(n) =
!
c
!c
!c
h(n) = cos(!0 n)
n=
n
!
N :N
n
!
c
n
c
N = 20
N = 40
h
y(n) = b0 x(n) + b1 x(n
H(z) = b0 + b1 z
1
1) + + bN
+ + bN
1z
1 (x
N + 1)
(N 1)
z
1
cfw_hn N
n=0
Hd (!) = R(!)ei(
!M )
ECE 310
University of Illinois at Urbana-Champaign
Profs. Bresler & Levinson
Homework 2
Reading: Chapter 2.1-2.6
Fall 2013
Due: Friday, September 13
1. Let x[n] be a signal with DTFT as shown in the following gure. Determine and sketch the
DTFT of y [n] =
University of Illinois, Urbana-Champaign
ECE 311: Digital Signal Processing Lab
1
Lab 2
Spectral Analysis
Solution
1
Sampling
Report Item: Assume you have an oscilloscope 8000 bytes of memory and each
sample requires 8 bytes. How many samples can you acqu
University of Illinois, Urbana-Champaign
1
ECE 311: Digital Signal Processing Lab
Lab 2
September 5, 2016
Spectral Analysis
INSTRUCTIONS:
All lab submissions include a written report and source code in the form of an m-le.
The report contains all plots, i
University of Illinois at Urbana-Champaign
ECE 311: Digital Signal Processing Lab
Lab 2: Solutions
Problem 1
Implement the DFT sum in Matlab, using the appropriate amount of zero padding. This may be done using two for
loops, or one for loop with a vector
University of Illinois at Urbana-Champaign
ECE 311: Digital Signal Processing Lab
Lab 6: Solutions
Problem 1
As evidenced by the table below, when increasing the length of a filter, the transition bandwidth is
narrower.
Rectangular (a)
Hamming (b)
Kaiser
University of Illinois at Urbana-Champaign
Department of Electrical and Computer Engineering
ECE 311: Digital Signal Processing Lab
LAB 1: Introduction to MATLAB
Spring 2014
1
Overview
The goal of this lab is to get familiar with MATLAB and to learn basic
University of Illinois at Urbana-Champaign
ECE 311: Digital Signal Processing Lab
LAB 1: Solutions
Problem 1
Parts (a) and (b)
The plots for Parts (a) and (b) are shown below. In part (a)i, the magnitude of z is 3.16 and the phase of z is 1.89
Part (a)i-(
University of Illinois at Urbana-Champaign
ECE 311: Digital Signal Processing Lab
Lab 4: Solutions
Problem 1
Part b
Assuming
the solutions are shown in Figure 1.
Impulse Response
Unit Step Response
1
35
0.9
30
0.8
25
0.7
0.6
20
0.5
15
0.4
0.3
10
0.2
5
0.1
University of Illinois at Urbana-Champaign
ECE 311: Digital Signal Processing Lab
Lab 7: Solutions
Problem 1
Parts a-c
Butterworth
Type I Chebyshev
0
Magnitude (dB)
Magnitude (dB)
200
0
-200
-400
-600
0
0.2
0.4
0.6
0.8
Normalized Frequency ( r ad/sample)
ECE311 Lab3 Report
Nuochen Lyu nlyu2
Report item1.1
The upper picture is
generated by the circular
convolution method.
The lower one is generated by
the normal convolution
method.
The result is the same.
The approximate
complexity of myDFTConv()
is Nlog(N
University of Illinois, Urbana-Champaign
ECE 311: Digital Signal Processing Lab
1
Lab 1
January 19, 2016
Matlab Overview
INSTRUCTIONS:
All lab submissions include a written report and source code in the form of an m-le.
The report contains all plots, imag
University of Illinois at Urbana-Champaign
Department of Electrical and Computer Engineering
ECE 311: Digital Signal Processing Lab
LAB 3: Windowing, Convolution and System Analysis
Spring 2012
1
Overview
In this lab we will study windowing, convolution,
University of Illinois at Urbana-Champaign
Department of Electrical and Computer Engineering
ECE 311: Digital Signal Processing Lab
LAB 5: Frequency Response of LSI systems
Spring 2012
1
Overview
In this lab we will use MATLAB to study the frequency respo
University of Illinois at Urbana-Champaign
Department of Electrical and Computer Engineering
ECE 311: Digital Signal Processing Lab
LAB 4: Difference Equations, z-Transforms, Pole-Zero Diagrams,
and BIBO Stability
Spring 2012
1
Overview
In this lab we wil
University of Illinois at Urbana-Champaign
Department of Electrical and Computer Engineering
ECE 311: Digital Signal Processing Lab
LAB 6: FIR Filter Design
Spring 2012
1
Overview
In this lab we will use MATLAB to design FIR lters using truncation, window
University of Illinois, Urbana-Champaign
ECE 311: Digital Signal Processing Lab
1
Lab 3
February 20, 2017
System Properties
INSTRUCTIONS:
All lab submissions include a written report and source code in the form of an m-le.
The report contains all plots, i
University of Illinois at Urbana-Champaign
Department of Electrical and Computer Engineering
ECE 311: Digital Signal Processing Lab
LAB 2: Frequency Representation and Spectral Analysis
Fall 2015
1
Objective
In this lab you will perform spectral analysis
Random
k
nk
pX (k )=
=np
e
k!
k
cfw_
1
,a u b
Uniform(a ,b) f x ( u )= ba
0 ,else
Exponential( )
np
Discrete
np(1p)
Discrete
1
p
Discrete
1p
2
p
Discrete
, for 0 k Discrete
n
Geometric ( p) pL ( k )=( 1 p )k1 p , for k 1
Poisson ( ) ,
E [ X2]
Discrete
(
Homework
1. (a) (b)
Magnitude = 3.1623
Angle = -1.2490
(c)
(d)
Both methods give us the same plot. It eliminates (unwraps) the discontinuity caused by the
range of the tangent inverse function. Therefore both methods achieve the same end result.
2.
The fu
University of Illinois at Urbana-Champaign
Department of Electrical and Computer Engineering
ECE 311: Digital Signal Processing Lab
LAB 1: Introduction to MATLAB
Fall 2015
1
Overview
The goal of this lab is to get familiar with MATLAB and to learn the bas
University of Illinois at Urbana-Champaign
Department of Electrical and Computer Engineering
ECE 311: Digital Signal Processing Lab
LAB 3: Sampling Eects and Windowing Eects
Fall 2015
1
Objective
The objective is to learn the sampling eects and the window
2. a.
X[k] = cfw_50.0000, -5.6569, -22.0000, 5.6569, -30.0000, 5.6569, -22.0000, -5.6569
The DFT is real because of the conjugate symmetry property.
b. The circular shift causes a linear phase shift in the Fourier domain.
c. Same as before, we see a linea
% Report Item1
clc, close all, clear all;
x = [1,4,-4,-3,2,5,-6]';
h = [1,2,3,4,5];
C = convmtx(h',7);
imagesc(C);
colorbar;
figure();
subplot(211);
a = stem(C*x);
subplot(212);
b = stem(conv(x,h);
% Report Item2.1
clc, close all, clear all;
x = [1,4,-4,-
1
University of Illinois, Urbana-Champaign
ECE 311: Digital Signal Processing Lab
Lab 7
April 19, 2016
Sample Rate Conversion
and Image Filtering
INSTRUCTIONS:
All lab submissions include a written report and source code in the form of an m-le.
The report
function y = sys2(x,a)
y(1) = 1;
for i = 2:64
y(i) = a.*y(i-1) + x(i).*x(i);
end
figure;
stem(y);
title(['impulse response when a = ',num2str(a)]);
end