Homework 8 (ECE220  Fall 2007)
•
Due:
Wednesday, November 7 by 2PM in the drop box outside 219 Phillips Hall.
•
Reasoning and work must be shown to gain full/partial credit.
•
WRITE YOUR NAME AND NET ID ON ALL PAGES HANDED IN!
1. (37 points) Consider the LTI system described by the RLC circuit shown in the below ﬁgure.
x
(
t
) is the input and
y
(
t
) is the output.
(a) (5 points) Find the diﬀerential equation that relates the input to the output.
(b) (10 points) Determine the frequency response of the system.
Let
R
= 1Ω,
C
= 1
F
, and
L
= 1
H
.
(c) (5 points) Determine the output of the system in part a) if the input is
x
(
t
) =
sin
(
t
).
(d) (5 points) Determine the output of the system in part a) if the input is
x
(
t
) =
cos
(2
t
+1).
(e) (12 points) Cascade the high pass ﬁlter introduced in class with the system to get the new
system (drawn below). Calculate the frequency response of the system when the input is
x
(
t
) and the output is
z
(
t
). Leave you answer as a function
R
,
L
, and
C
.
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View Full Document2. (18 points) Compute the Fourier Transform for the following signals.
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 Fall '05
 JOHNSON
 Signal Processing, spectral density, Autocorrelation, energy spectrum

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