ECE 301, Homework #5, due date: 9/28/2011
http://cobweb.ecn.purdue.edu/
∼
chihw/11ECE301F/11ECE301F.html
Question 1:
[Basic] p. 141, Problem 2.21 (b,d).
Question 2:
[Basic] p. 141, Problem 2.22 (a,e).
Question 3:
[Basic] This question is to verify the following two properties of the convolu
tion sum / integral:
•
Commutativity: (a) For an LTI system with
h
(
t
) = 2
U
(
t
+ 1)

2
U
(
t
), find out
the response
y
(
t
) when
x
(
t
) =
U
(
t
+ 1)
 U
(
t

1).
(b) For an LTI system with
h
(
t
) =
U
(
t
+1)
U
(
t

1), find out the response
y
(
t
) when
x
(
t
) = 2
U
(
t
+1)

2
U
(
t
).
Are your answers the same for the questions (a) and (b)?
•
Distributivity: (a) For an LTI system with
h
(
t
) = 2

3
t
U
(
t
), find out the response
y
(
t
) when
x
(
t
) = 2
U
(
t
+1)

2
U
(
t
) by computing the convolution integral
x
(
t
)
*
h
(
t
).
(b) For an LTI system with
h
(
t
) = 2

3
t
U
(
t
), find out the response
y
1
(
t
) when
x
1
(
t
) = 2
U
(
t
+ 1). Find out the response
y
2
(
t
) when
x
2
(
t
) = 2
U
(
t
).
Are your answers the same for the questions (a) and (b)?
Question 4:
[Basic] p. 144, Problem 2.28 (b,d,f,g).
Question 5:
[Basic] p. 144, Problem 2.29 (c,e,g).
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 Fall '06
 V."Ragu"Balakrishnan
 Digital Signal Processing, LTI system theory, Impulse response

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