Given or IIR filter defined by the difference equation(a) Determine the system function H(...

Given or IIR filter defined by the difference equation

(a) Determine the system function H(z). What are its poles and zeros?

(b) When the input to the system is three successive impulses

determine the functional form for the output signal y[n]. Assume that the ouput signal y[n] is zero for n<0.

Hint: Use linearity to find the output as the sum of three terms, each related to the impulse response of the system. Recall that the impulse response of first-order IIR filter has the form b0an for n ≥ 0.