Translations of spherical harmonics expansion coefficients for a sound field using plane wave expansions

A translation method for the spherical harmonics expansion coefficients of a sound field using plane wave expansions is proposed. It is based on the decomposition of a plane wave in the spherical harmonics domain and without the use of the spherical harmonics addition theorem, thus is very computationally efficient. Simulations are conducted for validation. The stabilities of the translations are compared with the conventional method in terms of matrix condition numbers. The proposed method is demonstrated to be more robust as the frequency increases and when upscaling the coefficients. Besides, the computation is much faster when high truncated orders are solved.