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Unformatted text preview: ECE 3250 HOMEWORK ASSIGNMENT II Fall 2009 For many of the problems, you might find the following geometricseries identities useful. In the equations, γ is a real or complex number. M X m =0 γ m = ( M + 1 if γ = 1 1 γ M +1 1 γ if γ 6 = 1 . Furthermore, ∞ X m =0 γ m = 1 1 γ when  γ < 1. In first six problems, find x 1 * x 2 . Please try to express your answer in the form x 1 * x 2 ( n ) = f ( n ) if n ≥ g ( n ) if n < , which is the same as x 1 * x 2 ( n ) = f ( n ) u ( n ) + g ( n ) u ( n 1) for all n ∈ Z . 1. x 1 = u and x 2 is the signal with specification x 2 ( n ) = 3 n u ( n ), n ∈ Z . 2. x 1 and x 2 are signals with specification x 1 ( n ) = 3 n u ( n ) and x 2 ( n ) = 7 n u ( n ) for all n ∈ Z . 3. x 1 and x 2 are signals with specification x 1 ( n ) = x 2 ( n ) = 5 n u ( n ) for all n ∈ Z . 4. x 1 and x 2 are signals with specification x 1 ( n ) = u ( n 1) and x 2 ( n ) = 3 n for all n ∈ Z ....
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