Consider a filter with transfer function

(a) Find the gain K so that this filter has unit dc gain. Use MATLAB to find and plot the magnitude response of H(z), and its poles and zeros. Why is it called a comb filter?

(b) Use MATLAB to find the phase response of the filter H(z). Why is it that the phase seems to be wrapped and it cannot be unwrapped by MATLAB?

(c) Suppose you wish to obtain an IIR comb filter that is sharper around the notches of H(z) and flatter in between notches. Implement such a filter using the function butter to obtain two notch filters of order 10 and appropriate cutoff frequencies. Decide how to connect the two filters. Plot the magnitude and phase of the resulting filter, and its poles and zeros.

-4 1+z¬4 1+ (1/16)z H(z) = K - -4