The second-order ARMA filter (cosine oscillator) has feedback coefficients a1= 1.414 and a2=-1 and feed forward coefficients b0=1 and b1 = -0.707. The value of the unit-sample response h3 = ________(x.xx).

Fill in the blank(s) with the appropriate word(s).


yi = 1.414yi-1 - yi-2 + xi - 0.707xi-1. With zero initial conditions and xi=di:
y0=d0 =1
y1 = 1.414y0 – d1 - 0.707d0= 1.414(1) - 0.707 = 0.707
y2 = 1.414y1 - y0- d2 – 0.707d1 = 1.414(0.707) -1 = 0
y3 = 1.414y2 - y1- d3 – 0.707d2 = 1.414(0) -0.707 = -0.707

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