HW4 - 4 n n ≥ 4 4 n n< 4 1 Problem 4.3 Consider a...

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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 310 Digital Signal Processing Problem Set 4 Fall 2003 Due: Wednesday, September 24, 2003 Problem 4.1 You are given y [ n ] = x [ n ] * h [ n ] = k = s k = -∞ h [ k ] x [ n - k ] , with h [ n ] = x [ n ] = 1 n = 1 2 n = 2 1 n = 3 0 else . 1. For what value of n is y [ n ] = 0? 2. Let S = { n : y [ n ] n = 0 } . Plot x [ n - k ] versus k for each n S . Graphically ±nd y [ n ] for each n S by multiplying { h [ k ] } by { x [ n - k ] } and summing. 3. Check your answer by computing { y [ n ] } via the 1-sided z-transform (applicable since both { x [ n ] } and { h [ n ] } are right-sided). Problem 4.2 Find y [ n ] = x [ n ] * h [ n ] for the following { x [ n ] } and { h [ n ] } : 1. x [ n ] = ( - 2) - n u [ n ] and h [ n ] = e - n u [ n ]. 2. x [ n ] = u [ - n ] and h [ n ] = nu [ n ] - nu [ n - 6]. 3. x [ n ] = b 1 n ≥ - 4 4 n n < - 4 and h [ n ] = b (1

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Unformatted text preview: / 4) n n ≥ 4 4 n n < 4 1 Problem 4.3 Consider a system with unit pulse response h [ n ] = (1 / 2) n ( u [ n ]-u [ n-5]). Determine the input { x [ n ] } 8 n =0 that will generate the output sequence: { y [ n ] } ∞ n =0 = { 1 , 2 , 2 . 5 , 3 , 3 , 3 , 2 , 1 , , , , . . . } . Problem 4.4 Find the z-transform, including the region of convergence, for each of the following sequences. 1. x [ n ] = ( 1 7 ) n u [ n ] 2. x [ n ] = ( 1 7 ) n u [-n-1] 3. x [ n ] = ( 1 7 ) n u [-n + 1] 4. x [ n ] = ( 1 7 ) | n | 2...
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HW4 - 4 n n ≥ 4 4 n n< 4 1 Problem 4.3 Consider a...

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