exam 2. 03doc

# exam 2. 03doc - University of Minnesota Dept of Electrical...

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University of Minnesota Dept. of Electrical and Computer Engineering EE 4541: Digital Signal Processing Fall 2003 Exam 2 December 4, 2003 _________________________________________________________________________ Name:_______________________________________ Student ID:___________________________________ Question 1 /8 Question 2 /8 Question 3 /14 TOTAL /30 Solve the three problems that appear on the next pages.

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2 Problem 1 Let x 1 (n) and x 2 (n) be zero outside the interval 0 n 99. Let y(n) be the 99 point circular convolution of x 1 (n) and x 2 (n) . If x 1 (n) is actually nonzero only for 10 n 39, determine the set of values of n for which y(n) is identical to the linear convolution of x 1 (n) and x 2 (n) .
3 Problem 2 A type II FIR filter with transfer function H II (z) and impulse response h II (n), is cascaded with a linear time invariant system with a transfer function (1-z -1 ). 1. Show that the resulting system is a generalized linear phase FIR filter and, 2. Determine its type.

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4 Problem 3 a) Let x(t) be zero for t <0 and t>100ms. Assume also for simplicity that X( Ω ) is bandlimited such that X( )=0 for | | > 2 π 10 4 rad/s , that is neglect any frequency content above . Further, let X(
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exam 2. 03doc - University of Minnesota Dept of Electrical...

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