exam_1 - University of Minnesota Dept. of Electrical and...

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University of Minnesota Dept. of Electrical and Computer Engineering EE 4541: Digital Signal Processing Fall 2006 Exam 1 October 26, 2006 _________________________________________________________________________ Name:_______________________________________ Student ID:___________________________________ Question 1 /10 Question 2 /10 Question 3 /10 TOTAL /30 Solve the three problems that appear on the next pages.
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2 Problem 1 a) A signal x(t) has a Fourier transform X( Ω ) that is zero except for 2/3 0 | | 0 . Determine the largest sampling interval T that can be used while guaranteeing that x(t) can be recovered exactly from the samples x(nT) , - n . [4 points]
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3 b) Consider the figure below. The filter H( ω ) is an ideal lowpass filter with gain 1 and cut-off frequency π /3 . For each of the following input signals x(n) determine whether the output x r (n) = x(n). Explain your reasoning. ω π/3 −π/3 Η(ω) 1 3 3 x(n) x r (n) i) x(n)= cos( n/4). [3 points]
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4 ii) x(n)= cos( π n/2). [ 3 p o i n t s ]
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5 Problem 2 The signal x(n) has a DTFT X( ω ) for which 3 () 0 , . 4 X π ωπ = ≤≤ (X( ) is of course periodic with period 2 .) We are given a sequence y(n) where 0 0 () , , ,.
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This note was uploaded on 10/30/2009 for the course EE 4541 taught by Professor Na during the Fall '06 term at Kentucky.

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exam_1 - University of Minnesota Dept. of Electrical and...

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