How to extract coupling matrix from S-parameter matrix

Can anyone tell me how to extract coupling matrix M from given S-parameter matrix of a filter, assuming given number of resonators (N) and known source and load values (R1, RN)? I cannot find formulas or numerical procedures.

hi...
i'm also searching for the same...
can u please share ur getherings with me?

What you want to do is an identification of black box filter as resonator coupled BPF ?

hi dear friend.
I've added an IEEE paper here. It gives you the idea of how to find a coupling matrix for given S parameter matrix.
I think , by using optimization methods , we can extract the coupling matrix from scattering matrix.
I'm trying to write a MATLAB code for extracting coupling matrix by using optimization methods.
there is a software named CMS , witch gives you the coupling matrix for desired filter response too.
but you should pay for it . you can find its demo version from its website.