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1. Let ??(??) = ??(??) + 2??(?? ? 1) ? ??(?? ? 3) and ?(??) =...

1. Let ??(??) = ??(??) + 2??(?? ? 1) ? ??(?? ? 3) and ?(??) = 2??(?? + 1) + 2??(?? ? 1) . Compute and plot each of the following convolutions:

(a) y1(n) = x(n) * h(n)

(b) y2(n) = x(n+2) * h(n)

(c) y3(n) = x(n) * h(n+2)

(d) Now consider the signal ??(??) = ( 1/ 3 ) ^(??) *?????? (( ?? /4)* ??) ??(??). Evaluate the z-transform of this signal and specify the corresponding region of convergence.

(e) Now consider the signal ??(??) = ( 1/ 3 )^(??)* ??(?? ? 3) . Evaluate the z-transform of this signal and specify the corresponding region of convergence.

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