Question: If the input x[n] to an LTI system is x[n] = u[n], the output is y[n] = (1/2) n1 u[n + 1]. (a) Find H(z),

If the input x[n] to an LTI system is x[n] = u[n], the output is 

y[n] = (1/2)n–1u[n + 1].

(a) Find H(z), the z-transform of the system impulse response, and plot its pole-zero diagram.

(b) Find the impulse response h[n].

(c) Is the system stable?

(d) Is the system causal?

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