Quiz3sol_FA08 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 410 Digital Signal Processing Quiz 3 Solution Thursday, October 02, 2008 Student Name: Prof. Jones (1pm), Prof. Bresler (3pm) INSTRUCTIONS You may not use any calculators, cell phones, earphones (or other forms of electronic media) for this quiz. You may use one side of one sheet of handwritten notes. Show all your work to get full credit for your answers. When you are asked to “ calculate ”, “ determine or “ fnd ”, this means providing closed-form expressions, without summation or integral expressions. Problem 1 (20 points) You are given a linear system and two input-output pairs: (The up arrow indicates the element at n = 0 in the sequence) x 1 [ n ]= { 1 , 2 }− y 1 [ n {− 2 , 3 , 3 , 5 } x 2 [ n { 2 , 1 y 2 [ n {− 1 , 1 , 3 , 3 } Determine the system’s response to input x [ n δ [ n ]and δ [ n 1], respectively. Is the system shift-invariant? Explain. Solution: Note: δ [ n 1 3 (2 x 2 [ n ] x 1 [ n ]) δ [ n 1] = 1 3 (2 x 1 [ n ] x 2 [ n ]) Because the system is linear, then: h [ n y [ n ] ± ± ± x [
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Quiz3sol_FA08 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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