Question

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 coefficients and b's are the denominator coefficients). Determine the magnitude response (in dB) at ω = π.

The filter coefficients of a second-order digital IR filter are: ao1, a2, a2 2, bo 1, b1- 1/2, b2- 1/8. (a's are numerator coefficients and b's are the denominator coefficients). Determine the magnitude response (in dB) at

Answer 1

"The General IIR difference Equation is sigm^N_l = 0 a_l y[n - l] = sigma^M_k = 0 b_k x[n - k] Given a_0 = 1, a_1 = - 2, a_2 = 2 b_0 = 1, b_1 = 1/2, b_2 = 1/8 In this sum a & b filter coefficient are from ""0 to 2"" Hence l = k doubleheadarrow varies from 0 to 2 Therefore sigma^2_l = 0 a_l y[n - l] = sigma^2_k = 0 b_k x[n - k] a_0 y[n] + a_1 y[n - 1] + a_2 y[n - 2] = b_0 x[n] + b_1 x[n - 1] + b_2 x[n - 2] apply 'z' transform on bothsides a_0 Y(z) + a_1 z^- 1 y(z) + a_2 z^- 2 y(z) = b_0 X(z) + b_1 Z^- 1 X(z) + b_1 Z^- 1 X(z) Y(z)/X(z) = b_0 + bz^- 1 + b_2 z^- 2/a_0"