# EE 207_101 Fall 2010 Graded HW 4 Due Date: Jan. 15, 2011 ```EE 207_101 Fall 2010
Due Date: Jan. 15, 2011
(groups of 2 students)
Problem 1:
A. For the circuit below, the switch is in open position before t = 0, then closed instantaneously at t =0.
1. Determine the initial capacitor voltage vC(0-) and the initial inductor current iL(0-).
2. Determine the output voltage across the capacitor, vC(t), using s-domain analysis.
closes at t = 0
S1
R1
5 ohm
R2
1 ohm
R3
4 ohm
+
-
Vs1
40V
L1
2 H
C1
1 F
B. Determine the inverse Laplace transform of each of the following function:
3e2 s
Y ( s) 
( s  1)( s  2)
Problem 2:
A signal is given by x(t )  5  6 cos 40 t .
1) x(t ) is sampled at sampling frequency f s 1  55Hz . Determine the spectrum of the sampled
signal, X s1 ( f ) , and plot it ( up to + 80 Hz). Can we reconstruct x(t) from its sample values x(n)? if
yes, explain how?
2) Repeat (1) with f s 2  35Hz . ( plot the spectrum up to 60Hz )
Problem 3:
The Z-Transofrm of a signal x(n) is given by:
with ROC: 0.5 | z | 3 , Find x(n) X (z ) 
5  8z 1
(1  0.5z 1 )(1  3z 1 )
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