# hw7 - y [ n ] that satisfy the following di±erence...

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ECE130B February 15, 2010 Home work 7 Due Date : Please turn it in by Monday, February 22, 2010, 5p.m. at the home work box. Reading . Chapter 2 of the text book. Exercise 1. Find explicit expressions for the following convolutions: 1. cos ( ω 0 n ) u [ n - 1] * sin ( ω 1 n + ϕ 1 ) u [ n - 2] . 2. p 1 2 P n +5 u [ n - 3] * p 2 3 P n - 1 u [ n + 7] . Exercise 2. Find all zero-input responses and all impulse-responses of the following di±erence equations: 1. α y [ n ] + β y [ n - 1] = x [ n ] , where α 0 . 2. y [ n ] - ( α + β ) y [ n - 1] + α β y [ n - 2] = x [ n ] , where α β . 3. y [ n ] - 2 α y [ n - 1] + α 2 y [ n - 2] = x [ n ] . You might want to add some of these solutions to your cheat sheet for the ²nals. Exercise 3. Find the output
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Unformatted text preview: y [ n ] that satisfy the following di±erence equations: 1. 10 y [ n + 1] + 50 y [ n ] + 60 y [ n-1] = p 7 10 P n +1 u [ n ] , with y [-2] = y [-1] = 0 . 2. y [ n-1] + y [ n ] + y [ n + 1] 3 = u [ n ] , with y [-2] = y [-1] = 0 . 3. y [ n ] + y [ n-2] = sin (6 πn / 10 ) u [ n ] , with y [-2] = y [-1] = 0 . Exercise 4. Find a y [ n ] that satis²es the di±erence equation y [ n ]-λy [ n-1] = λ n , with y [0] = 0 . (This is a bit tricky if you follow the recipe.) 1...
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## This note was uploaded on 04/06/2010 for the course ECE 130b taught by Professor Staff during the Winter '08 term at UCSB.

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