The module contains a function for performing the bilinear transform.
The input is a rational polynomial representation of the s-domain
function to be transformed.
In the bilinear transform, we substitute
2 1 - z^-1
s <-- -- * --------
ts 1 + z^-1
into the rational polynomial, where ts is the sampling period. To get
a rational polynomial back, we use the following method:
Substitute s^n with (2/ts * (1-z^-1))^n == [ -2/ts, 2/ts ]^n
Multiply the results by (1+z^-1)^n == [ 1, 1 ]^n
Add up all of the common terms
Normalize all of the coeficients by a0
where n is the maximum order of the numerator and denominator