Problem 5 An LTI system has unit impulse response h[n] = u[n] -u[n-2].

a.) Compute the system's function

$ H(z) = \sum^{\infty}_{k=-\infty} (u[k]-u[k-2])z^{-k} $

$ = 1 + 1/z \,\ $

b.) Use your answer in a) to compute the system's response to the input x[n] = cos(pi n)

$ cos(pi n) = (-1)^n \,\ $

and we plug that in into the previous equation and get it to be 0.

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Prof. Math. Ohio State and Associate Dean
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Jeff McNeal