Question: When the input to an LTI system is x[n] =(1/3) n u[n] + (2) n u[n 1], the corresponding output is y[n] = 5(1/3)

When the input to an LTI system is

x[n] =(1/3)n u[n] + (2)n u[–n – 1],

 the corresponding output is

y[n] = 5(1/3)n u[n] – 5(2/3)n u[n].

(a) Find the system function H(z) of the system. Plot the pole(s) and zero(s) of H(z) and indicate the region of convergence.

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

(c) Write a difference equation that is satisfied by the given input and output.

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

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