The second-order AR filter has feedback coefficients a1=0.9 and a2=0.5 (b0 = 1). When xi = sin(2?i/8), the value of y2 = ________(x.xx).
Analysis: x0=sin(0)=0, x1=sin(?/4)=0.707, x2=sin(?/2)=1. yi = 0.9yi-1 +0.5yi-2 + xi. With zero initial conditions:
y0=x0 =1
y1=0.9y0+x1=0.9(1) + 0.707 = 1.607
y2=0.9y1+0.5y0+x2 = 0.9(1.607) + 0.5(1)+ 1 = 2.9463 = 2.95
0.95
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