A3

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Signals and Systems Issued: 4 September 2013 Fall 2013 Due: 11 September 2013 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) = 1.5 x ( k + 1) 0.5 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 3 2 6 E E + { x ( k )} 3. Find the operational transfer function for each of the following simulation diagrams:
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