[aguirreSL]

Adds to pytta.functions the conversion between the power series of a memoryless nonlinearity and the harmonics it produces, as ita_nonlinear_power_to_harmonic_series and ita_nonlinear_harmonic_to_power_series of the ITA-Toolbox, following Dietrich, Uncertainties in acoustical transfer functions (2013), sec. 3.3:

1. power_to_harmonic_series(coefficients, gain=1, phase=0): the amplitudes of the harmonics 1 to N that y = Σ a_k x^k gives for a cosine of amplitude gain, divided by gain as the sweep deconvolution does, with harmonic m turned by (m - 1) phase. The coefficients go along the first axis and may be arrays, converted entry by entry.
2. harmonic_to_power_series(harmonics, gain=1, phase=0): the inverse.

The amplitudes come from the Chebyshev expansion of cos^k (numpy.polynomial.chebyshev.poly2cheb). Two points differ from the ITA-Toolbox:

1. For a gain other than 1 the ITA-Toolbox divides once more by the gain (order k scaled by G^(k-2)); this implementation scales by G^(k-1), which gives the amplitudes of the example in Dietrich (2013), p. 51. With gain=1, the default, both agree.
2. The ITA-Toolbox shifts the frequency axis of each order (ita_nonlinear_shift_frequency_vector) when it converts spectra of an itaAudio; here the arrays are converted entry by entry and no axis is shifted.

The ITA code was read for its semantics only and nothing was copied.

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

1. y = x + x² + x³ + x⁴ driven with G = 1/2 gives 1.1875, 0.3125, 0.0625 and 0.0156, the values of Dietrich (2013), p. 51.
2. For six random coefficients the harmonics equal the DFT of the polynomial of a cosine over one period, divided by the gain (7.3e-17).
3. The phase of harmonic m is (m - 1) phase, as the ITA-Toolbox gives, and the inverse returns complex coefficients given per frequency (9.0e-16).

Checked with Python 3.12, numpy 1.26 and scipy 1.17, and against the ITA-Toolbox in MATLAB R2026b for the gain and phase conventions. 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