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Material Type: Project; Class: Discrete Systems; Subject: Electrical Engineering; University: Morgan State University; Term: Fall 2003;
Typology: Study Guides, Projects, Research
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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] = (− 12 )nu[n − 4], h[n] = 4 nu[2 − n]. For the sake of this problem, assume that x[n] and h[n] are defined for − 10 ≤ n ≤ 10.
Problem 2 Consider the two discrete-time signals x[n] and h[n] given by x[n] = u[n] − u[n − 50], h[n] = 5 δ[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 k=
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]
then the sum can be written as an inner product
y[n] = HT^ X[n].