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:

1. Substitute s^n with (2/ts * (1-z^-1))^n == [ -2/ts, 2/ts ]^n
2. Multiply the results by (1+z^-1)^n == [ 1, 1 ]^n
3. Add up all of the common terms
4. Normalize all of the coeficients by a0

where n is the maximum order of the numerator and denominator