PROBLEM #1: This problem consists of three parts. (a) Find the transfer function and the difference equation for a stable 2nd-order filter that has unity d.c. gain, but for which the input x(k) = cos(km/6) produces a large forced response. (Your filter will have a lightly damped resonance at the given frequency, and H(1) = 1.) (b) Plot the frequency response of the filter. (c) Plot the time-domain response of the filter to the given input sequence x1(k) = cos(kr/6). Also plot the time-domain response of the filter to the input sequence x2(k) = cos(kr/6) + cos(kn/12) + 1. Make sure the time-domain results are consistent with the frequency response plots. PROBLEM #1: This problem consists of three parts. (a) Find the transfer function and the difference equation for a stable 2nd-order filter that has unity d.c. gain, but for which the input x(k) = cos(km/6) produces a large forced response. (Your filter will have a lightly damped resonance at the given frequency, and H(1) = 1.) (b) Plot the frequency response of the filter. (c) Plot the time-domain response of the filter to the given input sequence x1(k) = cos(kr/6). Also plot the time-domain response of the filter to the input sequence x2(k) = cos(kr/6) + cos(kn/12) + 1. Make sure the time-domain results are consistent with the frequency response plots