EECE 359 MATLAB Exercise 2 1 Introduction 2 Discrete-time ...

EECE359: Matlab Exercise 2 1
1 Introduction
EECE 359
MATLAB Exercise 2
This assignment gives Matlab examples for the material covered in Chapter 2 of the Lecture
Notes. Commands indicated by the >> should be typed in the Matlab Command
Window. The Matlab built-in help command provides a lot of useful information. For example,
to find out how to use the Matlabconv command, just typehelp conv in the Matlab
Command Window.
This exercise builds on the previous Matlab exercise, so please have a look at it if you
have not already done so.
2 Discrete-time Convolution
Matlab has built-in support for discrete-time convolution using the conv function. Before
trying the exercises below, consult the Matlab help, i.e. try running help conv. It turns out
that conv can be used for other things besides discrete-time convolution. What is its other
use?
2.1 Convolution of two impulses
In this section, we will examine the result of a convolution of two impulses, e.g. y[n] =
δ[n]∗δ[n − 1]. First, create the variables (we will create them on the time axis n = [0, 1, 2]):
>> x1 = [1 0 0];
>> x2 = [0 1 0];
Now, we can convolve them, and create the proper time vector for the output
>> y = conv(x1,x2);
>> t = 0:length(y)-1;
And, to see the result graphically, let’s plot the output:
>> stem(t,y);
What can you observe about the output of this system? Try changing the times the two
impulses occur. What happens to the output of the system? Try changing the order of
convolution, i.e. try conv(x2,x1). Does this change the output?

EECE359: Matlab Exercise 2 2
2.2 Convolution of an impulse and a square wave
In this section, we will examine the result of a convolution y[n] = δ[n − 1]∗xs[n], were
xs[n] =
Enter the following code to create this signals
>> x = [0 1 0 0 0 0];
>> xs = [1 1 1 1 1 1];
1, 0 ≤ n ≤ 5
0, otherwise
Now, convolve the signals and create a time vector:
>> y = conv(x,xs);
>> t = 0:length(y)-1;
Try plotting the output of the system using stem. What can you observe about the output?
Try shifting the time square wave and/or the impulse. How does this change the
convolution output?
2.3 Convolution of two square waves
In this section, we will try convolving two square waves together. We use again the
function xs[n] defined in Equation 1, and look at the convolution y[n] = xs[n]∗xs[n].
Create xs as we did above. Now, we can perform the convolution:
>> y = conv(xs,xs);
>> t = 0:length(y)-1;
Plot the output using thestem function as we did before. What can you observe about the
convolution of two square waves?
3 Animated Discrete-Time Convolution
In this section, you will learn to create Matlab script files (called M-files), and you will write
a Matlab script which shows an animation of the convolution process. The signals we are
convolving are from page 36 of the Lecture Notes.
3.1 Creating an M-file
Create a new M-file (“File” → “New” → “M-File”), and enter the following code into it (the
line numbers at the left margin are only for reference, and should not be entered in the
file):
(1)

EECE359: Matlab Exercise 2 3
1 clear all; close all;
2
3 % Example from p. 36 of Lecture Notes
4 t = [-4 -3 -2 -1 0 1 2 3 4];
5 x = [ 0 0 0 0 1 2 3 0 0];
6 h = [ 0 0 0 0 2 1 0 0 0];
7 y = [ 0 0 0 0 0 0 0 0 0];
8
9 yc = 1;
10
11 for n=min(t):max(t),
12 pause(3);
13
14 % flip h
15 ht = fliplr(h);
16
17 if n

EECE359: Matlab Exercise 2 4
3.2 Running the M-file
Use the “Current Directory” window in your Matlab session to change the directory to the
one in which you saved your “animate.m” file.
Now, typeanimate into your Matlab Command Window. This will execute the code you
created in the file “animate.m”. Assuming you copied the code from Section 3.1 properly,
you should see a display window appear with two plots, and demonstrate graphically the
process of convolution.
3.3 Explanation of the Code
Below you will find an explanation of some new Matlab concepts used in the M-file given
in Section 3.1.
• Line 1: clear all removes all previously created variables, and close all closes
all open plot windows.
• Line 11–40: this is a Matlab for loop, which ends with end. The value of n takes on
all integer values from min(t) to max(t). The Matlab functions min and max return
the minimum and maximum values in a vector, respectively.
• Line 12: pause(3) causes Matlab to stop and wait for 3 seconds.
• Line 15: fliplr reverses the contents of a vector → v old= [v1, v2, . . .,vn] to be → v new=
[vn, vn−1, . . .,v1]
• Lines 17–23: this is a Matlab if,then,else structure.
• Lines 19,22: we create a new (temporary) vector by adding zeros at the left or the
right (as required)
• Line 25: this is the actual convolution sum. Note that we are doing the convolution
one step at a time, so we can’t use the Matlab conv function.
• Lines 28, 37: subplot creates two plots inside one plotting window (see the Matlab
help for more details)
• Lines 30,32: hold allows you to “plot-over” an already-existing plot (this is how we
create the overlay of two different functions in the upper plot)
• Lines 33,34,35,39: xlabel, legend, title are various Matlab commands to add text
to your plot. See the help for more details.