Question: Question 1 ( 35 marks ) An infinite impulse response (IIR) filter is designed by using an analog prototype filter, which is described by the

Question 1 ( 35 marks ) An infinite impulse response (IIR) filter is designed by using an analog prototype filter, which is described by the following s-domain transfer function, H(s): 1 H(s)= (S) s' +5s5+4 (a) Using the Impulse Invariance Method, find the z-domain transfer function, H(z) of the IIR filter using a sampling interval of f; = SHz. Show your work. (b) Find the pole(s) of the transfer function of the IIR filter. (c) On the z-plane, plot and label the pole(s) of H(z). (d) Is the TIR filter stable? Explain by referring to your answers from Parts (b) and (c). (e) Derive the filter's time-domain difference equation. Show your work. (f) Draw the IIR filter's structure diagram using signal processing operational symbols

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