GEORGIA INSTITUTE OF TECHNOLOGY
SCHOOL of ELECTRICAL and COMPUTER ENGINEERING
ECE 2025
Summer 2008
Problem Set #5
Assigned:
Week of 16Jun08
Due Date:
23/24Jun08
=
⇒
Please check the “Announcements” section on Tsquare often.
All official course
announcements are posted there.
ALL
of the
STARRED
problems will have to be turned in for grading. A solution will be
posted to the web.
Your homework is due in recitation at the beginning of class.
After the beginning
of your assigned recitation time, the homework is considered late and will be given a zero.
PROBLEM 5.1
*:
Suppose a particular linear timeinvariant system is described by the difference equation
y
[
n
] = 3
x
[
n
] +
x
[
n

2]

2
x
[
n

3]
.
(a) (2 pts) Determine the response of this system to a unit impulse input; i.e., find the
output
y
[
n
] =
h
[
n
] when the input is
x
[
n
] =
δ
[
n
].
Make a stem plot of
h
[
n
] as a
function of
n
.
(b) (1 pt) This system is a causal FIR filter. Determine the filter coefficients
{
b
k
}
.
(c) (7 pts) Suppose the input to this system is
x
[
n
] =
0
for
n <
0
n
+ 1
for
n
= 0
,
1

n
for
n
= 2
,
3
3
for
n
≥
4
Compute the values of
y
[
n
], over the range 0
≤
n
≤
12. Perform the computations by
drawing up a “convolution table.” You will probably find it easiest to make a table
with three rows that you need to sum. Make stem plots of both
x
[
n
] and
y
[
n
].
PROBLEM 5.2
:
Which ever way you set up the convolution table in Problem 5.1(c), set it up the other
way, and make sure you get the same answer.
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PROBLEM 5.3
*:
The diagram in Fig. 1 depicts a
cascade connection
of two linear timeinvariant systems;
i.e., the output of the first system is the input to the second system, and the overall output
is the output of the second system.
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 Spring '08
 JUANG
 Digital Signal Processing, Signal Processing, pts, LTI system theory, Impulse response

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