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**Unformatted text preview: **University of Minnesota Dept. of Electrical and Computer Engineering EE 4541: Digital Signal Processing Fall 2003 Exam 1 October 23, 2003 _________________________________________________________________________ Name:_______________________________________ Student ID:___________________________________ Question 1 /10 Question 2 /10 Question 3 /10 TOTAL /30 Solve the three problems that appear on the next pages. 2 Problem 1 (a) The discrete signal x(n) = 3 cos( π n/4) + 7 sin( π n/2) was obtained by sampling the continuous time signal x(t) = 3 cos(10 π t) + 7 sin(20 π t) with a sampling time T . Determine two values of T that are consistent with this information. 3 (b) Consider the system shown below. C/D H( ω ) D/C T T x(t) x(n) y(t) y(n) Suppose that the signal x(t) has a Fourier transform X( Ω ) such that X( Ω )= 0 for | Ω | > 2 π 10 4 . For what range of T is the structure above equivalent to an analog low pass filter with cut-off frequency Ω c ? That is, for what range of T, is y(t) a lowpass version of x(t) ? 4...

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