1
EEGR 322: Discrete Systems
FALL 2003
Project 1
Due date: Monday, October 13, 2003
In this project, all the questions are supposed to be answered using MATLAB. Some basic infor-
mation on the use of MATLAB for the study of discrete signals can be obtained in the following
web sites
http://www.eece.unm.edu/signals/ and http://www.jhu.edu/˜signals/
When you are asked to sketch the graph of a signal, do not forget to clearly label the
axis.
Problem 1
Consider the two discrete-time signals x[n] and h[n] given by
x[n]=(−1
2)nu[n−4],
h[n]=4nu[2 −n].
For the sake of this problem, assume that x[n] and h[n] are defined for −10 ≤n≤10.
1. Use MATLAB to define x[n].
2. Use MATLAB to define h[n].
3. Use the appropriate MATLAB function to compute y[n] = x[n]∗h[n] (for which values of n
is y[n] defined?).
4. On the same page sketch the graphs of x[n], h[n] and y[n] (hint: use the subplot command).
Problem 2
Consider the two discrete-time signals x[n] and h[n] given by
x[n] = u[n]−u[n−50],
h[n]=5δ[n]+4δ[n−1] + 3δ[n−2] + 2δ[n−3]+δ[n−4].
For this particular problem, the convolution sum can be expressed as
y[n] = h[n]∗x[n] =
M−1
X
k=0
h[k]x[n−k], where M = 5.
We want to evaluate the above sum for any value of n. If we consider the following vectors
H=
h[0]
h[1]
.
.
.
h[M−1]
and X[n] =
x[n]
x[n−1]
.
.
.
x[n−M+ 1]
