Question 1\ (a) Analyse the filter given by

H(z)=((1-e^(j\\\\theta _(z))^(-1))(1-e^(-j\\\\theta _(z))^(-1)))/((1-re^(j\\\\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 fiter does

H(2)

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

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

(include the block diagram).

(a) Analyse the filter given by H(z)=(1rez1)(1rejz1)(1ejz1)(1ejz1) 1. Find the poles and zeroes of this system. Explain how r affects the system stability. ii. Assume r=0.75 and =4. Sketch the magnitude response. Which type of fiter does H(2) represent - low pass, high pass, band pass or band stop? (b) Design an IIR filter based on the analog filter given by Hc(s)=(s+1)(s+2)2 (include the block diagram)