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Unformatted text preview: ECE 3250 HOMEWORK ASSIGNMENT IV Fall 2009 1. A certain discrete-time LTI system with system mapping S has impulse response h with specification h ( n ) = 3- n 2 u ( n ) for all n Z . (a) Suppose that x is a bounded signal, and that S ( x ) = y . Suppose d is another bounded signal that acts as a disturbance at the input. Suppose k d k = . Find an upper bound on the effect of the disturbance at the output when we use x = x + d as input, i.e., find an upper bound on k S ( x )- y k . (b) Can you find a disturbance d with k d k = that causes the inequality you found in (a) to hold with equality? 2. In each case, determine whether the convolution of x 1 and x 2 exists. In any instance where it does exist, just say why you know it exists you dont have to compute it. In any instance where it doesnt exist, please show why by trying to compute it. (a) x 1 = u and x 2 is the signal with specification x 2 ( t ) = e 3( t- 7) u ( t- 7) for all t R ....
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This note was uploaded on 03/26/2010 for the course ECE 3250 at Cornell University (Engineering School).