Using Hilbert Transform Code

I am attempting to calculate the hilbert transform of

𝑍(𝜏,𝜔)=1/(1+(𝜏𝜔)^2)

with respect to 𝜔 for various values of 𝜏, using a given code:

function h = hilb1(F, N, b, y)

    n  = [-N:N-1]';                        %  Compute the collocation points ...
    x  = b*tan(pi*(n+1/2)/(2*N));
    FF = eval(F);                          %  ... and sample the function.

    a  = fft(fftshift(FF.*(b-1i*x)));       %  These three lines compute the
    a  = exp(-1i*n*pi/(2*N)).*fftshift(a);  %  expansion coefficients.
    a  = flipud(1i*(sign(n+1/2).*a))/(2*N);

    z  = (b+1i*y)./(b-1i*y);                 %  The evaluation of the transform
    h  = polyval(a,z)./(z.^N.*(b-1i*y));    %  reduces to polynomial evaluation
                                           %  in the variable z.

with an output in the ranges of: omega_vec = logspace(-4, 4, 81)

A brief explanation of the code can be found here: http://appliedmaths.sun.ac.za/~weideman/research/hilbert.html

However, being new to this area of maths and to Matlab, I do not know where to start.

I understand that I should plug in the above function into F, and used the run function on Matlab to test out other known inputs and values.

However, given the information above I am unsure of what N, b, and y should be? I have experimented with multiple values but most result in some sort of error.

Apologies for what could be an elementary question; I am very much a beginner to both the content and to the code and would greatly appreciate a breakdown of how to approach this task or what the code is even doing.