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ECE 130A: Signal Analysis and Processing
Prof. Michael Liebling
Fall 2010
TAs: Jingning Han, Hari Sivakumar
Distribution: Monday, 22 November 2010
Homework Due:
Wednesday, 1 December 2010 at 7:00 p.m.
University of California, Santa Barbara
Homework 8
Problem 1: System Function Algebra for Interconnected LTI
Systems (40 Points)
The input
x
(
t
) and output
y
(
t
) of a causal LTI system are re
lated through the block diagram representation shown on the
right.
(a)
Determine a differential equation relating
y
(
t
) and
x
(
t
).
(b)
Is this system stable?
+
+
+
+
1
2
1
s
1
s
1
6
x
(
t
)
y
(
t
)
Problem 2: Systems with Feedback (30 Points)
A causal LTI system
S
with input
x
(
t
) and output
y
(
t
), as depicted below, is characterized by the following
differential equation:
d
d
t
y
(
t
)
+
2
y
(
t
)
=
1
10
x
(
t
)
x
(
t
)
y
(
t
)
S
(a)
Find the output if the input is
x
(
t
)
=
cos2
t
.
(b)
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This note was uploaded on 12/06/2010 for the course ECE 130A taught by Professor Madhow during the Fall '07 term at UCSB.
 Fall '07
 MADHOW

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