Polynomial Multiplication of Bilinear Transform

This approach uses polynomial multiplication (convolution indeed) to implement bilinear transform...

% use polynomial multiplication to computer bilinear transform
% the input is H(s) in decending order polynomial
% the output is H(z) in decending order polynomial
%
% Usage : [c,d] = mBilinear(a,b,Fs);
% with a: vector in decending order of H(s) numerator
% b: vector in decending order of H(s) denumerator
% c: H(z) numerator in decending order
% d: H(z) denumerator in decending order
% Fs: sampling frequency
%
% Note: vector a and b must have the same length. The highest order of
% H(z)'s numerator and denumerator are scaled to be 1. This is
% different to Matlab's bilinear function. For example:
% [c,d] = mBilinear([0 1 1],[1 0 1],1) will return
% c = [1.0000 0.6667 -0.3333] and d = [1.0000 -1.2000 1.0000]
% while using Matlab's bilinear function,
% [p,q ] = bilinear([0 1 1],[1 0 1],1) will return
% p = [0.6000 0.4000 -0.2000] and q = [1.0000 -1.2000 1.0000]
% It is obvious that c = p/p(1);

An C-version bilinear transform is also available.