Question: When the input to a linear time-invariant system is x [n] = 5u[n], the output is y[n] = [2 () n + 3 ( )

When the input to a linear time-invariant system is

x [n] = 5u[n],

 the output is 

y[n] = [2 (½)n + 3 (– ¾)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 of the system for all values of n.

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

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