Answer Happy

PROBLEM #3 Pole-Zero Placement FD Methods A digital filter is characterized by the following: It is a low pass filter and has one pole and one zero. The zero is at a distance r 1.5 from the origin of the Z domain and the pole is at a radius 0.75 High frequency signals do not pass through this system. Answer the following: 1) Plot the pole-zero pattern of the filter, justify your selections of poles and zeros. 2) Normalize the frequency response so that H(0) = 1 and determine H(z). 3) Determine the systems impulse response. 4) Determine H(w) and its magnitude and phase response. 5) Find the difference equation representing his filter. 6) Compute the output of the filter if x(n) = 4 + 2 cos (h + 2 cos(in) for all n. 7) Give Magnitude plot and decide on the quality of the design. 8 Comment on your answers of part 6 using your argument of part 7 and understanding of the filter. πη | در