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