Transformation Between Uniform Linear and Spherical Microphone Arrays With Symmetric Responses

Spherical microphone arrays are suited for phase mode processing, which complements spatio-temporal processing and often simplifies both the understanding and development of different beamforming techniques. Since a spherical geometry cannot benefit directly from methods specially developed for uniform linear arrays, the weight and algorithm design for spherical arrays is mostly optimized and found numerically. One of the exceptions is a recent study that develops the well-known Dolph-Chebyshev weights in the phase mode framework. We show that for the case of a symmetric response, the spherical and linear array geometries are one-to-one, related through a herein developed linear transformation. With this transformation, uniform linear array specific processing techniques become readily available in closed form for spherical array processing. Any uniform linear array weight design technique can be directly applied to spherical arrays. We also show how this transformation can be used to generate virtual uniform linear array data from spherical array data, enabling us to apply uniform linear array specific adaptive algorithms to spherical arrays.