aspcol.sphericalharmonics.translation_operator

aspcol.sphericalharmonics.translation_operator(pos, wave_num, max_order_input, max_order_output)

Translation operator for harmonic coefficients, such that shd_coeffs(pos_orig + pos) = T(pos) @ shd_coeffs(pos_orig)

Defined according to $T = hat{S}^T $, where $hat{S}$ is the basis translation matrix defined in [martinMultiple2006]. This definition is consistent with the definition (6) in [uenoSound2018].

Parameters:

  • pos (ndarray of shape (num_pos, 3)) – position argument to the translation operator

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

  • max_order_input (int) – maximum order of the coefficients that should be translated

  • max_order_output (int) – maximum order of the translated coefficients

Returns:

T – translation operator, such that shd_coeffs(pos_orig + pos) = T(pos) @ shd_coeffs(pos_orig)

Return type:

ndarray of shape (num_freqs, num_pos, num_coeffs_output, num_coeffs_input)

References

[martinMultiple2006] P. A. Martin, Multiple scattering: Interaction of time-harmonic waves with N obstacles, vol. 107. in Encyclopedia of mathematics and its applications, vol. 107. Cambridge, UK: Cambridge University Press, 2006. [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.