Question 1\ (a) Analyse the filter glven by

H(z)=((1-e^(j\\\\theta )z^(-1))(1-e^(-j\\\\theta )z^(-1)))/((1-re^(\\\ ho \\\\theta )z^(-1))(1-re^(-j\\\\theta )z^(-1)))

.\ i. Find the poles and zeroes of this system. Explain how

r

affects the system stability.\ ii. Assume

r=0.75

and

\\\\theta =(\\\\pi )/(4)

. Sketch the magnitude response. Which type of filter does

H(z)

represent - low pass, high pass, band pass or band stop?\ (b) Design an IR filter based on the analog fiter Given by

H_(n)(s)=(1)/((s+1)(s+2))

(include the block diagram).

(a) Analyse the fitter given by H(z)=(1rez1)(1rejz1)(1ez1)(1ejz1) 1. Find the poles and zeroes of thits system. Explain how r affects the system stability. 17. Assume r=0.75 and =45. Sketch the magnitude response. Which type of filter does H(z) represent - low pass, high pass, band pass or band stop? (b) Design an UR filter based on the analog fiter given by Hc(s)=(s+1)(s+2)1 (include the block diagram)