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Unformatted text preview: ECE 3250 HOMEWORK ASSIGNMENT III Fall 2009 1. A certain LTI system has impulse response h whose specification is h ( n ) = 5- n if 0 ≤ n < 7 otherwise . (a) What is D h , the set of all x ∈ F Z for which Conv h ( x ) exists? (b) Find the output S ( x ) of the system when the input is the signal x whose specifi- cation is x ( n ) = 3 for all n ∈ Z . (c) Find S ( u ), the step response of the system, which is the output of the system when its input is a unit step. What I’d like here are formulas for S ( u )( n ) for all n ∈ Z . (d) Suppose x ∈ F Z has duration 13. What is the maximum possible duration for S ( x )? 2. Denote by S the system mapping for the causal sliding-window M-fold averager with M = 5. (a) Find a non-constant signal x ∈ F Z for which S ( x )( n ) = 11 for every n ∈ Z . (b) Show that lim n →∞ S ( x )( n ) = 0 for every left-sided signal x ∈ F Z . Show also that lim n →-∞ S ( x )( n ) = 0 for every right-sided signal x ∈ F Z ....
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This note was uploaded on 03/26/2010 for the course ECE 3250 at Cornell.