Question: Consider a linear time-invariant system whose system function is (a) Suppose the system is known to be stable. Determine the output y[n] when the input

Consider a linear time-invariant system whose system function is

(a) Suppose the system is known to be stable. Determine the output y[n] when the input x[n] is the unit step sequence.

(b) Suppose the region of convergence of H(z) includes z = ?. Determine y[n] evaluated at n= 2 when x[n] is as shown in Figure.

(c) Suppose we wish to recover x[n] from y[n] by processing y[n] with an LTI system whose impulse response is given by h_i[n]. Determine h_i[n]. Does h_i[n] depend on the region of convergence of H(z)?

-2 I(z) (1--1) (1- 3z-) Part B

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