[aguirreSL]

Adds the modal model of a rectangular room of ita_roomacoustics_analytic_FRF (ITA-Toolbox) to pytta.rooms:

1. rectangular_room_frf(dimensions, source, receiver, frequencies, T=2, f_max=None): the transfer function p / Q (Pa per m³/s) from a point source of volume velocity Q to a receiver, in a room with rigid walls and uniform modal damping, by modal superposition (Fahy, Foundations of Engineering Acoustics, 9.8):

   H = jω ρ c² Σ ψ_N(r) ψ_N(r0) / (Λ_N (ω_N² - ω² + 2 j δ ω)),

   with cosine eigenfunctions, Λ_N = V Π (1 for n = 0, 1/2 otherwise), and δ = 3 ln(10) / T for every mode. The time dependence is exp(jωt), the convention of numpy.fft, so the impulse response is causal. The uniform mode (0, 0, 0) is computed in closed form, ρ c² / (V (2δ + jω)), so that the response is finite at 0 Hz, where it is the compression of the whole volume.

2. rectangular_room_ir(dimensions, source, receiver, samplingRate, numSamples, T=2, f_max=None): its impulse response as a SignalObj. The modes go up to 0.4 times the sampling rate by default, and a raised-cosine fade takes the response to zero at the Nyquist frequency. Cutting it where it is large would ring through the whole circular response.

The model was written from Fahy and checked by the rules below. The ITA function returns a pole-residue object, and its own code notes that a correction factor in it is not totally correct, so it was not used as the oracle.

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

1. In a room of 5 m × 4 m × 3 m, the (1, 0, 0) mode peaks at 34.317 Hz (c / (2 Lx) = 34.320 Hz) with a half-power bandwidth of 1.0990 Hz, against 3 ln(10) / (π T) = 1.0994 Hz.
2. Swapping source and receiver leaves the transfer function unchanged, and a receiver on the nodal plane x = Lx / 2 is 35.9 dB below a receiver at the wall at that mode.
3. The decay curve of the energy summed over six receivers gives T = 0.7920 s for a model with T = 0.8 s, and the response keeps falling, 149 dB down from 2.0 s to 2.5 s.
4. Positions outside the room are 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