Spring EE350 2007 - Exam 3
27 April 2007
Name: ________________________
EE 350 Signals and Systems
Spring 2007
Exam #3
One 8 x 11 sheet of notes, and a calculator are allowed during the exam.
Write all answers neatly and show your work to get full credit.
Rationalize all complex fractions.
A calculator is allowed during the exam, but should not be needed.
Write neatly and WATCH YOUR ALGEBRA!
Problem 1
Problem 2
Problem 3
/30
/30
/40
Total
/100
Homework average to date:
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Course grade to date:
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Lab quiz average to date:
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Lab average to date:
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Lab course grade to date:
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EE350 Spring 2007 - Exam 3
27 April 2007
Name: ________________________
1. (30 points) You are given a signal, x(t),
4
x(t)
a(t)
X
H1(j)
b(t)
+
c1(t)=cos(100t)
d(t)
X
e(t)
H2(j)
y(t)
c2(t)=cos(200t)
The spectrum for the real signal x(t) is shown below:
2
X(jw)
-40
-10 10
40
and the filters
H1(j)
H2(j)
1
3
-150
150
a. (6 points) Draw and fully label A(j).
b. (6 points) Draw and fully label B(j).
c. (6 points) Draw and fully label D(j).
d. (6 points) Draw and fully label E(j).
e. (6 points) Draw and fully label Y(j).
-100 -90
90 100
EE350 Spring 2007 - Exam 3
Name: ________________________
27 2007
2. April (30 points) Z-Transforms
a. (6 points each) Determine the Z-transform of the following signals.
x[n] 2
1
-1
0
i)
-1
ii)
1
2
n
-(-1/4)n u[n+2]
b. (8 points) Determine the transfer function for the following system. Show your work!!
2y[n] - 1/4y[n-2] = 3x[n]+x[n-1]
c. (10 points) Using the transform tables 10.1 & 10.2 determine the inverse transform of
1 7 z 1
6
1/3< |z| < 1/2
X ( z) =
1 1
1 + 6 z 1 z 2
6
EE350 Spring 2007 - Exam 3
27 April 2007
Name: ________________________
3. (40 points) A signal is
sin(3t )
cos(2t )
3t
(a) (10 points) What is the equation describing X(j)? Show your work and explain
your steps clearly! (Dirac deltas, unit steps or piece wise defined is fine. Simplify!)
x(t ) = 5
(b) (10 points) Draw & fully label |X(j)|.
(c) (10 points) According to Nyquist,
(i)
What is the smallest sampling frequency, s, that may be used to sample
x(t) so that full reconstruction is possible? Explain clearly how you got
your answer.
What is the Nyquist rate?
(ii)
(iii) What is the Nyquist frequency?
(d) (10 points) If this signal is sampled at twice the Nyquist rate you derived above,
sketch and label a representative part of the spectrum of the sampled signal, x(nT).