[aguirreSL]

Adds to pytta.functions the two fits of ita_prony_analysis of the ITA-Toolbox, which give the coefficients of an IIR filter from a measured response:

1. prony(h, nb, na): Prony's method in the time domain (Parks and Burrus, Digital Filter Design, 1987). The denominator fits the samples after nb by least squares, and the numerator then matches the first nb + 1 samples exactly.
2. invfreqz(H, w, nb, na, weights=None): the linear equation error fit in the frequency domain of Levi, "Complex curve fitting", IRE Trans. Automatic Control 4(1), 1959, which minimizes Σ weights |B(w) - H(w) A(w)|², as MATLAB's invfreqz without iterations. SciPy has no such function.

Both return b and a with a[0] = 1; scipy.signal.tf2zpk(b, a) gives the zeros and poles that ita_prony_analysis returns. The ITA-Toolbox calls MATLAB's invfreqz and, for the time domain, pdi_prony, a copy of MATLAB's prony; neither was ported, and both functions here are written from the references.

The tests in tests/test_prony.py recover known filters and print the largest relative difference of the coefficients:

1. prony recovers a filter with three zeros and the five poles of a Chebyshev type I filter from 200 samples of its impulse response (9.0e-14).
2. invfreqz recovers a fourth-order Butterworth filter from its response at 512 frequencies (1.2e-14).

Checked with Python 3.12, numpy 1.26 and scipy 1.17. The 7 failures of development (3 in test_h5io.py, 4 in test_pyttasave.py) are the same with and without this change.

Co-Authored-By: Claude Fable 5.1 noreply@anthropic.com