Spring ECE350 2011 - Exam 2
8 April 2011
Name: ________________________
EE 350 Signals and Systems
Spring 2011
Exam #2
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
Problem 4
/15
/25
/30
/30
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 Exam 2, Spring 2011
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ECE350 Spring 2011 - Exam 2
8 April 2011
Name: ________________________
1) (15 points) Determine the Fourier series coefficients for a periodic function with T=2 and
x(t)=e-t
0 < t <2 .
Simplify your answer.
EE350 Exam 2, Spring 2011
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ECE350 Spring 2011 - Exam 2
8 April 2011
Name: ________________________
2) (25 points) For a periodic function with period T=, the non-zero Fourier series coefficients
are
a0 = -1, a2 = a*-2 = ej/4
(a) (10 points) Express the function x(t) in form
x(t) the = Akcos(kt+k)
i.e., a sum of cosines with varying magnitudes and phases
(b) (15 points) If x(t) is passed through a real filter with
H(j) =
2
1 + 4 j
what are the Fourier series coefficients of y(t) (call them bk)?
EE350 Exam 2, Spring 2011
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ECE350 Spring 2011 - Exam 2
8 April 2011
Name: ________________________
3) (30 points) Determine the value of y(t) when
x(t) = 4e-t u(t)
h(t) = e-2t u(t)
(a) (15 points) By convolving x(t) and h(t). Integration is required for this answer to be
complete.
(b) (15 points) By taking the Fourier Transform of x(t) and h(t).
EE350 Exam 2, Spring 2011
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ECE350 Spring 2011 - Exam 2
8 April 2011
Name: ________________________
4) (30 pts) For the system
y" + 6y' + 8y = 3x(t)
a. (6 points) Find the frequency response H(j) using eigen function methods.
b. (6 points) Find H(j) using Fourier transforms,
c. (8 points) Invert H(j) to find the impulse response.
d. (8 points) Draw and fully label the magnitude of the straight line Bode plot describing this
system.
e. (2 points) What type of filter is this? Explain why you gave this answer.
EE350 Exam 2, Spring 2011
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