ACS 513  DIGITAL SIGNAL PROCESSING
Fall 2010
Homework #2
Assigned:
9/7/2009
Due:
9/16/2009
1.
Consider the sequence {
x
[
n
]} = {1, 2, 3,2, 1}.
a.
Assume the sequence starts at
n
= 0, and write an expression for
x
[
n
] as a sum
of scaled and delayed discrete delta functions (i.e.
a
m
[
nm
] ).
b.
Assume the sequence starts at
n
= 0, and write an expression for
x
[
n
] as a sum
of scaled and delayed unit step functions (i.e.
a
m
u
[
nm
] ).
c.
Assume the sequence starts at
n
= 2, and write an expression for
x
[
n
] as a
sum of scaled and delayed discrete delta functions (i.e.
a
m
[
nm
] ).
d.
Assume the sequence starts at
n
=+2, and write an expression for
x
[
n
] as a sum
of scaled and delayed unit step functions (i.e.
a
m
u
[
nm
] ).
2.
For each of the following systems, determine whether the system is (1) stable, (2)
causal, (3) linear, (4) timeinvariant, and (5) memoryless:
a.
]
[
)
cos(
]}
[
{
n
x
n
n
x
T
,
b.
]
1
[
]
[
]
1
[
]}
[
{
n
x
n
x
n
x
n
x
T
c.
]
[
]}
[
{
n
x
e
n
x
T
d.
b
n
ax
n
x
T
]
[
]}
[
{,
a
and
b
constants
Please justify your answer for each property and each example.
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 Spring '10
 BROWN
 Digital Signal Processing, LTI system theory, Impulse response, unit step functions, discrete delta functions

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