Problem (3) a. A Biomedical signal x(n) that is observed in an experiment is modeled as a noisy version of a desired signal d(n) as x(n) = d(n) + n(n). The noise process n is a zero-mean, 2 unit-variance random process with uncorrelated samples (white noise, with ACF On(t) = o(t) that is statistically independent of the = signal process d. The ACF of Cact) is given by the sequence {0.5, 0.3,0.1}, for t = 0,1,2, respectively. Prepare the Wiener-Hopf equation and derive the coefficients of the optimal Wiener filter. [3 marks] b. A biomedical signal sampled at 400 Hz was found to have a significant amount of 50 Hz interference. (a) Design a notch filter with two zeros to remove the interference. (b) Design a comb filter with four and eight zeros to remove the interference. Compare the results in a and b. (c) What is the effect of the filter if a signal sampled at 100 Hz is applied as the input? [3 marks) a