Question

A causal second order IIR digital filter is described by the difference equation: y(n) = -a₁y(n - 1) - a₂y(n - 2) + b₀x(n) + b₁x(n - 1) + b₂x(n - 2), is excited by an input signal, which is given by:

x(n) = 2sin (πn + 5π/6).
Some of corresponding output values y(n) are given by table 1. it is assume that b₀ = a₂ and a₁ = b₁.
n y(n)
0 0.81
1 -0.98
2 1.17
3 -0.86
4 0.99
5 -1.12
Plot the magnitude respone |H(eʲʷ)|.

Answer 1

To plot the magnitude response of a second-order IIR digital filter, the transfer function must be derived from the difference equation, followed by calculating the magnitude response over a range of frequencies.

Step-by-step explanation:

The student's task involves analyzing a second-order Infinite Impulse Response (IIR) digital filter described by a specific difference equation. When the filter is excited by an input signal, output values are obtained and given in a table. The magnitude response |H(ejω)| of the filter is typically plotted using frequency on the x-axis and magnitude on the y-axis. The information provided in the question does not suffice to plot the magnitude response; however, it would involve calculating the frequency response of the filter from the difference equation and then plotting its magnitude.

In practice, one would calculate the Z-transform of the difference equation to find the transfer function H(z) of the filter. After substituting z with ejω, the magnitude response would be computed for a range of frequencies. Hence, to plot the magnitude response |H(ejω)|, the filter's transfer function is needed along with its coefficients and a range of frequency values to analyze.