A3

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Signals and Systems Issued: 3 September 2014 Fall 2014 Due: 10 September 2014 Homework Assignment #3 1. Iterate by hand to find the first few values of y ( k ) for the following difference equations: (a) y ( k 1) y ( k ) x ( k ), y (0) 0, x ( k ) 0 , 0 0 , 1 k k . (b) y ( k 1) y ( k ) 0, y (0) 1. (c) y ( k 2) y ( k 1) 2 y ( k ) x ( k 1) x ( k ), y (0) y (1) 0, x ( k ) 0 , 0 0 , 1 k k . (d) y ( k 2) y ( k 1) 2 y ( k ) 0, y (0) 1, y (1) 0. 2. For each difference equation or operational relation, draw a corresponding simulation diagram having the minimum possible number of delay blocks: (a) y ( k 1) y ( k ) x ( k ) (b) y ( k 2) y ( k 1) 2 y ( k ) x ( k 1) x ( k ) (c) (E 2 1){ y ( k )} (E 2){ x ( k )} (d) { y ( k )} 4 5 2 6 2 2 E E E E { x ( k )} (e) { y ( k )} 3 2 2 6 E E E { x ( k )} 3. Find the operational transfer function for each of the following simulation diagrams: (a) (b) (See Problem 4 on reverse.)
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