Question: When the input to a linear time-invariant system is x[n] = (1/2) n u[n] + (2) n u[n 1], the output is y[n] =

When the input to a linear time-invariant system is 

x[n] = (1/2)n u[n] + (2)n u[–n – 1],

the output is

y[n] = 6(1/2)n u[n] – 6 (3/4)n u[n].

(a) Find the system function H(z) of the system. Plot the poles and zeros of H(z), and indicate the region of convergence.

(b) Find the impulse response h[n] of the system for all values of n.

(c) Write the difference equation that characterizes the system.

(d) Is the system stable? Is it causal?

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