[aguirreSL]

Adds to pytta.functions the filters of the ITA-Toolbox ita_butterFR, ita_liriFR, ita_filter_LiRi, ita_filter_notch and ita_filter_peak:

1. butterworth(signal, cutoff, btype='low', order=8, linkwitz_riley=False, zero_phase=False): a low-pass, high-pass or band-pass Butterworth filter, or a Linkwitz-Riley filter (a Butterworth filter of half the order, squared), optionally keeping only the magnitude.
2. notch(signal, fc, Q=2): the second-order notch of the Audio EQ Cookbook of R. Bristow-Johnson, as ita_filter_notch.
3. peak_eq(signal, fc, gain, Q=2): the second-order bell filter of ita_filter_peak (bilinear design with K = tan(π fc / fs) and V = 10^(gain / 20)).

As in the ITA-Toolbox, the filters act on the spectrum of the signal, so they are circular. The response is evaluated at the FFT bins of the signal. ita_butterFR samples it with MATLAB freqz(Hd, nBins), which spaces nBins points from 0 to π without π, so its bins sit slightly off the FFT bins. For that reason the tests check the rules of each filter and do not compare with ITA.

ita_make_filter and ita_filter_pdi are left out. They wrap the general fractional octave filter of the ITA-Toolbox, which pytta.OctFilter covers.

The tests in tests/test_filters.py print the measured values:

1. The Butterworth filters of order 2, 4 and 8 are 3.0103 dB down at the cut-off, and from 2 fc to 4 fc they fall as |H|² = 1 / (1 + (f / fc)^(2n)) predicts (11.80, 24.07 and 48.18 dB).
2. A Linkwitz-Riley pair of order 4 is 6.0206 dB down at the crossover, and its low-pass and high-pass sum to a flat magnitude within 5.1e-8.
3. The notch is zero at fc (6.2e-9) and 1 at DC, and the peak filter has its gain at fc (6.0000 dB) and 1 at DC and Nyquist.
4. The zero-phase response is real, and an unknown type or an odd Linkwitz-Riley order is rejected.

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