Solved: Problem 1 [25 points]: An FIR filter of length 3 is defined by the sys

Question

Problem 1 [25 points]: An FIR filter of length 3 is defined by the system function H(z) = h[0]+h[1]z¯¹+h[2]z¯². It exhibits a symmetric impulse response; that is, h[0] = h[2]. Let the input to this filter be a sum of two cosine sequences of angular frequencies 0.3 rad/samples and 0.6 rad/samples, respectively. (a) Determine the impulse response coefficients h[0], h[1] so that the filter passes only the low frequency component of the input. [15 points] HINT: Use DTFT definition to show that |H(e)| = |H(z)|ze| = 2h[0] cos 0+h[1]. Setup two equations for the two conditions: |H(e10.3)| = 1,|H(e/0.6)| = Oand solve for the two unknown impulse response coefficients. SOLUTION: h[0] = h[2] =? h[1] =? (b) Plot the magnitude and phase spectra of the designed filter in part (a) above using MATLAB. [10 points] HINT: You may use MATLAB freqz(b,a) function.