Question

1.The filter coefficients of a second-order digital IIR filter are: a₀ = 1, a₁ = -2, a₂ = 2, b₀ = 1, b₁ = 1/2, b₂ = 1/8. (a's are numerator coefficents and b's are the denominator coefficients). Compute the magnitude response |H(e^jω)| where ω = 5.174 rad/sec.

2.

It is desired to extract a constant signal s(n)= s from the noisy measured signal x(n)= s(n)+v(n)= s + v(n), where v(n) is zero-mean white Gaussian noise of variance ϭ_v². For that purpose, the following IIR lowpass filter is used:

H(z)= b/(1- az^-1), H(e^jω)= b/(1- a e^-jω) , |H(e^jω)|² = b²/(1- 2a cos(ω) + a²)

where a and b are arbitrary constants (0 < a < 1). Estimate the value of the cut-off frequency ω_c if a = 0.08.

Answer 1