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University of California at Berkeley
Department of Electrical Engineering and Computer Sciences
Professor J. M. Kahn, EECS 120, Fall 1998
Final Examination, Wednesday, December 16, 1998, 58 pm
NAME:
Problem 1
(15 pts.) The
equivalent noise bandwidth
of a CT LTI system
is deﬁned
as:
.
Find the value of BW for the system having the following impulse response.
ht
(29
FT
↔
H j
ϖ
BW
1
2
π

Hj
ϖ
2
0
2

ϖ
d
∞
–
∞
∫
=
t
2
1

1
0123456
0 for
t
0 and
t
6
<
=
Note to students in Fall 99:
Only problems 1, 2, 5, 6 would be appropriate for your Midterm 2.
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Problem 2
(25 pts.) The CT LTI system shown here can model many simple situations that produce
echoes. Here,
K
and
∆
are real constants, and
.
(a)
(10 pts.) Find an expression for the impulse response
.
(b)
(10 pts.) For what values of
K
is the system stable? Justify your answer.
(c)
(5 pts.) Let
, and assume
. Sketch
.
∆
0
≥
xt
(29
yt
Σ
+
+
gain
K
delay
∆
delay
∆
ht
K
1
–
=
ut
2
∆
–
–
=
3
Problem 3
(40 pts.) Consider a DT system described by the difference equation:
.
(a)
(5 pts.) Sketch a realization of this system using only two delay elements.
(b)
(5 pts.) Find the transfer function
.
(c)
(5 pts.) Plot the poles and zeros and indicate the region of convergence of
.
(d)
(5 pts.) Is the system BIBO stable? Justify your answer.
yn
[]
1
–
2
2
–
–
+
xn
1
–
+
=
Hz
(29
Re
z
{}
Im
z
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(e)
(5 pts.) Find the impulse response
.
(f)
(5 pts.) Let the input be
,
. Find
,
.
(g)
(10 pts.) Let the input be
,
. (If you are interested in the initial conditions,
they are fully speciﬁed by our speciﬁcation of the input signal.) Find
,
. Explain why,
as
,
doesn’t agree with the result found in part (f).
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This note was uploaded on 05/17/2009 for the course EE 120 taught by Professor Ayazifar during the Spring '09 term at University of California, Berkeley.
 Spring '09
 Ayazifar
 Electrical Engineering

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