aspcol.sphericalharmonics.shd_basis

aspcol.sphericalharmonics.shd_basis(pos, order, degree, wavenum)

Spherical harmonic basis function for sound field in 3D

Implements: sqrt(4pi) j_order(kr) Y_order^degree(polar angle, zenith angle) degree and order of the spherical harmonics might be swapped according to some definitions.

Parameters:

  • pos (ndarray of shape (num_pos, 3)) – positions of the evaluation points

  • order (ndarray of shape (num_coeffs,)) – order of the spherical harmonics. Can be any non-negative integer

  • degree (ndarray of shape (num_coeffs,)) – degree of the spherical harmonics. Must satisfy |degree[i]| <= order[i] for all i

  • wave_num (float or ndarray of shape (num_freq,)) – wavenumber, defined as w / c where w is the angular frequency and c is the speed of sound

Returns:

f – values of the spherical harmonic basis function at the evaluation points

Return type:

ndarray of shape (num_freq, num_coeffs, num_pos)

Notes

See more detailed derivations in any of: [brunnstromBayesianSubmitted] J. Brunnström, M. B. Møller, and M. Moonen, “Bayesian sound field estimation using moving microphones,” IEEE Open Journal of Signal Processing, submitted. [uenoSound2018] N. Ueno, S. Koyama, and H. Saruwatari, “Sound field recording using distributed microphones based on harmonic analysis of infinite order,” IEEE Signal Process. Lett., vol. 25, no. 1, pp. 135–139, Jan. 2018, doi: 10.1109/LSP.2017.2775242.