[aguirreSL]

Adds four DSP utilities that the ITA-Toolbox has and PyTTa lacks (ita_groupdelay, ita_coherence, ita_cepstrum and ita_icepstrum, ita_generate_mls). The ITA code was read for its semantics only and nothing was copied.

1. pytta.group_delay(signal): group delay of each channel in seconds, at signal.freqVector. It uses the derivative of the spectrum, tau = Re{DFT(n x[n]) / DFT(x[n])} / fs, which needs no phase unwrapping.
2. pytta.coherence(x, y, winSize=1024): magnitude squared coherence from scipy.signal.coherence, with a Hann window and 50 % overlap. Channels are paired one to one, and a one-channel signal is paired with every channel of the other.
3. pytta.cepstrum(signal, kind='complex') and pytta.icepstrum(cepstrumObj, delay): real and complex cepstrum and the inverse complex cepstrum. As in Oppenheim and Schafer, section 13.5, the integer linear phase is removed before the complex cepstrum and returned, so that icepstrum can put it back. The magnitude floor is the same as in minimum_phase ([FEATURE] add minimum_phase for SignalObj #56), but this branch does not depend on [FEATURE] add minimum_phase for SignalObj #56.
4. pytta.generate.mls(order, samplingRate) and pytta.mls_deconvolution(response, order): one period of a symmetrical maximum length sequence from scipy.signal.max_len_seq, and the impulse response from the response to that sequence played periodically. The deconvolution is a periodic cross-correlation normalized by L + 1 (Peltonen 2000, eq. 2.14 to 2.22). With more than one period, the first is dropped and the others are averaged.

The tests in tests/test_dsp_utilities.py print the measured differences:

1. The group delay of a delay of 37 samples is 37/fs (error 1.6e-14 samples), and that of a first order allpass with a = 0.8 matches its analytic expression (error 9e-8 samples).
2. The coherence of y = h * x + white noise matches SNR / (1 + SNR) within 9.7e-3, and a signal against itself gives 1.
3. The cepstra of (1 - 0.9 z^-1)(1 + 0.6 z^-1) match the analytic series -(a^n + b^n)/n within 3.8e-8 (complex) and 1.9e-8 (real).
4. A mixed phase FIR delayed by 7 samples goes through the complex cepstrum and back with an error of 3.8e-8.
5. The periodic autocorrelation of an MLS of order 10 is (L + 1) delta - 1, exactly.
6. A FIR of 40 taps excited by three periods of an MLS of order 12 is recovered within 1.0e-4, below 1/L. The remaining difference is the constant -sum(h)/(L + 1) of the method, which was checked to 4e-8.

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