Question: A causal LTI system has impulse response h [n], for which the z-transform is, (a) What is the region of convergence of H (z)? (b)

A causal LTI system has impulse response h [n], for which the z-transform is,

1+ H(2) = %3D (1-+1)(1-f - 1) Part C y[r] = -}(-1)"u[n]

(a) What is the region of convergence of H (z)?

(b) Is the system stable? Explain.

(c) Find the z-transform X(z) of an input x[n] that will produce the output,

y[n] = ? 1/3(?1/4)nu[n] ? 4/3(2)nu[?n ? 1].

(d) Find the impulse response h[n] of the system.

1+ H(2) = %3D (1-+1)(1-f - 1) Part C y[r] = -}(-1)"u[n] - {(2)"u[-n - 1].

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