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Signals and Systems Exam - Spring 2011 - Prof. Charles P. Baylis, Exams of Signals and Systems

Information about a university exam for the course elc 3335 - signals and systems, held in spring 2011. The exam is closed-book and closed-notes, and lasts for 1 hour and 15 minutes. It covers topics related to fourier series and fourier transforms. Problem statements and instructions for the exam.

Typology: Exams

2010/2011

Uploaded on 12/20/2011

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Name_____________________________________________
ELC 3335 – Signals and Systems
Spring 2011
Test 2 – April 7, 2011
Closed Book/Closed Notes/Formula Sheet Provided
1 hour and 15 minutes
1. The exam is closed-book/closed-notes. Only the formula sheet provided with the exam may be used.
2. A calculator may be used to assist with the test. No laptops or PDAs are allowed. No cellular phones
may be used in any way during the test. Unauthorized electronic device use will result in
disqualification.
3. You must circle or box your answers to get full credit.
4. All work and steps toward a solution must be clearly shown to obtain credit.
5. Partial credit may be given provided that the grader can clearly follow your work to the extent that an
understanding of the problem is demonstrated.
6. No collaboration is allowed on this examination. Only the exam proctor may be consulted for
clarification.
7. You may attach extra sheets to the exam if necessary. Each page should contain your name, the
problem number, and the page number for that problem.
Please sign the statement below. YOU MUST SIGN THE STATEMENT OR YOU WILL GET A ZERO
FOR THIS EXAMINATION!!!
I hereby testify that I have neither provided or received information from unauthorized sources during the
test and that this test is the sole product of my effort.
Signed ________________________________________ Date_____________________
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Name_____________________________________________

ELC 3335 – Signals and Systems Spring 2011 Test 2 – April 7, 2011 Closed Book/Closed Notes/Formula Sheet Provided 1 hour and 15 minutes

  1. The exam is closed-book/closed-notes. Only the formula sheet provided with the exam may be used.
  2. A calculator may be used to assist with the test. No laptops or PDAs are allowed. No cellular phones may be used in any way during the test. Unauthorized electronic device use will result in disqualification.
  3. You must circle or box your answers to get full credit.
  4. All work and steps toward a solution must be clearly shown to obtain credit.
  5. Partial credit may be given provided that the grader can clearly follow your work to the extent that an understanding of the problem is demonstrated.
  6. No collaboration is allowed on this examination. Only the exam proctor may be consulted for clarification.
  7. You may attach extra sheets to the exam if necessary. Each page should contain your name, the problem number, and the page number for that problem.

Please sign the statement below. YOU MUST SIGN THE STATEMENT OR YOU WILL GET A ZERO FOR THIS EXAMINATION!!!

I hereby testify that I have neither provided or received information from unauthorized sources during the test and that this test is the sole product of my effort.

Signed ________________________________________ Date_____________________

PROBLEM 1 (25 points) : Consider the periodic function f ( t ):

t

(a) (5 points) Find the value of a 0 in the cosine/sine trigonometric Fourier series.

(b) (10 points) Find the value of a (^) n (in terms of n for n ≥1).

(continued on next page)

PROBLEM 2 (20 points) : The trigonometric Fourier series of a certain periodic signal is given by

⎟+ + ⎛^ +

⎟+ ⎛^ +

= + ⎛^ −

f(t) 2 5 cos t π^ cos t π cos t cos t^ π

(a) (7 points) Sketch the trigonometric Fourier series spectra (that is, provide plots of Cn and θn versus ω ). Clearly label all radian frequencies, amplitudes, and phases of the spectral components on your plots.

(b) (6 points) From the trigonometric spectral plots, plot the exponential Fourier series magnitude and phase spectra. Clearly label all radian frequencies, amplitudes, and phases of the spectral components on your plots.

(c) (7 points) By inspection of the plot in part (b), write the exponential Fourier series expression for f(t).

PROBLEM 4 (15 points): Use Table 4.1 and Table 4.2 to find the Fourier transform of the following function f ( t ). Do not use the definition; use an appropriate pair from Table 4.1 and an appropriate property from Table 4.2.

f ( t )

t

PROBLEM 5 (20 points): Determine the Nyquist sampling rate and the Nyquist sampling interval for the signal f ( t ) = 2 sinc^2 (10π t ) sinc (4π t )