🚀 go-pugleaf

It sounds like a good application for "Frequency Domain Least Squares" system 
identification.  Inputs are frequency response values (magnitude and phase) at 
a number of discrete frequencies from DC to one-half the sampling frequency 
(for filters having real coefficients), or from DC to the sampling frequency 
(for filters having complex coefficients).  Outputs are coefficients of a 
transfer function of the form:

                    -1           -n
            b  + b z  + ... + b z
             0    1            n
    H(z) = --------------------------
                    -1           -m
             1 + a z  + ... + a z
                  1            m

Causality is assumed, stability is not necessary.  You have total control over
"m" and "n", so you can model an all-zero system, an all-pole system, or a
pole-zero system.  Both magnitude and phase are modeled.  The algorithm is
VERY good at finding discrete equivalents for continuous-domain filters, which
is what it sounds like you are trying to do.

Your friendly university library should have, or be able to get, these:

    G. Berchin, R. Roberts, and M.A. Soderstrand; "A New Model-Based Parameter
    Estimation Technique for Use in Deconvolution"; Proceedings of the 1986
    Asilomar Conference on Signals, Systems, and Computers; Pacific Grove, CA,
    November 1986.

    G. Berchin, M.A. Soderstrand, and R. Roberts; "Deconvolution Using
    Model-Based Parameter Estimation", Proceedings of the 30th Midwest
    Symposium on Circuits and Systems; Syracuse NY, August 1987.

    G. Berchin and M.A. Soderstrand; "A Total Least-Squares Approach to
    Frequency Domain System Identification"; Proceedings of the 32nd Midwest
    Symposium on Circuits and Systems; Urbana IL, August 1989.

If not, or if you need any help with the algorithm, contact me through the net.

        Greg Berchin