GEORGIA INSTITUTE OF TECHNOLOGY
SCHOOL of ELECTRICAL and COMPUTER ENGINEERING
ECE 2025
Summer 2010
Problem Set #5
Assigned:
21Jun10
Due Date:
28Jun10
Please check the Tsquare chat and announcements daily. All official course announcements will
be posted there.
ALL
of the
STARRED
problems should be turned in for grading.
Homework is due at the
start
of your recitation.
After this assignment is handed in by everyone, a solution to all the starred problems will be posted
to the web.
PROBLEM 5.1
*:
Suppose a particular linear timeinvariant system is described by the difference equation
y
[
n
] = 2
x
[
n

1]

7
x
[
n

3] + 4
x
[
n

5]
.
(a) 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) This system is a causal FIR filter. Determine the filter coefficients
{
b
k
}
.
(c) Suppose the input to this system is
x
[
n
] =
0
for
n <

1
2
n
for
n
=

1
,
0
,
1

n
for
n
= 2
,
3
1
for
n
≥
4
Compute the values of
y
[
n
], over the range

3
≤
n
≤
13.
Perform the computations by
drawing up a “convolution table.” You will probably find it easiest to make a table with four
rows that you need to sum. Make stem plots of both
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 Summer '08
 JUANG
 Digital Signal Processing, Signal Processing, LTI system theory, Impulse response, difference equation

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