HW01_F10 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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Unformatted text preview: UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 410 Digital Signal Processing Problem Set 1 Fall 2010 Reading: Chapter 1, Appendices 1 and 2 Prof. Bresler, Prof. Hasegawa-Johnson August 27, 2010 Problem 1 Evaluate and represent your final answer in both Cartesian and Polar forms. Try to simplify as far as you can by hand, without using a calculator or computer. (a) (3 150 ) + (5 60 ) + (4 120 ) (b) ( 1 + j ) 5 1 + j (c) 5 60 2 j + 2 e j 2 j (d) ( 1 + j 3 1 j + 3 + j 1 j 2 ) n Problem 2 Sketch the following functions: (a) n ( u [ n ] u [ n 5]) (b) u [ n + 2] u [ n 3] (c) u [ n 1] + nu [ n 4] Where the u [ n ] is the step function in the discrete time domain, n . Problem 3 Compute the following: (a) Determine the roots of the equation 2 z 3 + 1 = 0 (b) Use the roots to factor the polynomial G ( z ) = 2 z 3 + 1 as a product of first order in z....
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HW01_F10 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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