Optimal Higher Order Ambisonics Encoding with Predefined Constraints

In this paper, we propose a design method for 3-D higher order ambisonics (3-D HOA) encoding matrices which offers the possibility to impose spatial stop-bands in the directivity patterns of all the spherical-harmonic audio channels while keeping the transformed audio channels still compatible with the 3-D HOA reproduction sound format. This might be useful as an encoding technique which suppresses interfering signals from specific directions in a 3-D HOA recording, or in other situations where certain spatial areas should be suppressed. The design method is adapted from recent work on the optimization of spherical microphone array beamforming. Using the proposed optimization method and the spherical harmonics mathematics framework, the relationship between several design factors, e.g., distortions in the desired response, the dynamic range of matrix coefficients, can be analyzed and illustrated as function of frequency. Based on the proposed optimization formulation, additional constraints can also be easily included and solved. In some of the formulations, the processing can be applied as a matrix multiplication to recorded spherical harmonics coefficients, that is, already encoded 3-D HOA format signals. The modified signals can be of the same or a lower spherical harmonics order. For a full optimization that gives a globally optimal solution, on the other hand, the processing must be applied to the microphone signals themselves. Numerical and experimental results validate the proposed method.