TT-Net: Dual-path transformer based sound field translation in the spherical harmonic domain

In the current method for the sound field translation tasks based on spherical harmonic (SH) analysis, the solution based on the additive theorem usually faces the problem of singular values caused by large matrix condition numbers. The influence of different distances and frequencies of the spherical radial function on the stability of the translation matrix will affect the accuracy of the SH coefficients at the selected point. Due to the problems mentioned above, we propose a neural network scheme based on the dual-path transformer. More specifically, the dual-path network is constructed by the self-attention module along the two dimensions of the frequency and order axes. The transform-average-concatenate layer and upscaling layer are introduced in the network, which provides solutions for multiple sampling points and upscaling. Numerical simulation results indicate that both the working frequency range and the distance range of the translation are extended. More accurate higher-order SH coefficients are obtained with the proposed dual-path network.