Determine and plot the frequency characteristics of the

Question

Question: Consider two filters with transfer functions given by

H₁(z) = 1 + 2z^-1 + 3z^-2 + 2z^-3 + z^-4 and

H₂(z) = 1 + 2z^-1 + 3z^-2 + 2z^-3 - z^-4

(i) Determine and plot the frequency characteristics of the filters.

(ii) If the sequence x[k] cos(0.5k) + cos(k) is applied at the input of filter H1(z), determine the output of the filter from the frequency characteristics obtained in (i).

(iii) Repeat (ii) for filter H2(z). What advantage do you see with the linear-phase filter?