We present a comparison of the measured and theoretical performance of a dual co-centred spherical microphone array that consists of an open spherical microphone array with a smaller, rigid spherical microphone array at its centre. The dual co-centred spherical microphone array has 64 microphones, with 32 microphones on the open spherical microphone array of radius 6.30 cm and 32 microphones on the rigid spherical microphone array of radius 1.63 cm. We have previously shown  that this even distribution of microphones, between the two spherical microphone arrays, provides a greater frequency range of operation for a third-order, 64-channel spherical microphone array compared to a single rigid 64-channel spherical array. The performance of the dual co-centred spherical microphone array is measured in an anechoic chamber using a speaker mounted on a robotic arm. A comparison is made between the theoretical and measured directivity pattern for various frequencies.  A. Parthy, C. Jin, and A. van Schaik "Optimisation of Co-centred Rigid and Open Spherical Microphone Arrays," in Proc. of 120th Audio Engineering Convention, Paris, France, May 20-23, 2006.
"In , Rafaely derives the spatial aliasing error and the measurement noise error for a SMA in a plane-wave soundfield with the array looking in the direction of the plane-wave, as is common in the literature. Using Rafaely's error formulation we demonstrate in  that our dual, concentric SMA is accurately described by these errors in practice as well as in theory. "
[Show abstract][Hide abstract] ABSTRACT: We present a new method and performance data related to volumetric acoustic intensity imaging using a spherical microphone array (SMA) consisting of a dual, concentric rigid and open SMA. The dual, concentric array was designed to improve the frequency range of a standard SMA. We apply standard techniques associated with interior spherical near-field acoustic holography (NAH) and, in particular, consider issues related to the optimal use of information from both arrays for NAH projection and the advantages that thus accrue from utilising a dual, concentric SMA.
Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009, 19-24 April 2009, Taipei, Taiwan; 01/2009
[Show abstract][Hide abstract] ABSTRACT: Spherical Microphone Arrays (SMAs) constitute a powerful tool for analyzing the spatial properties of sound fields. However, the performance of SMA-based signal processing algorithms ultimately depends on the physical characteristics of the array. In particular, the range of frequencies over which an SMA provide rich spatial information is conditioned by the size of the array, the angular position of the sensors and other factors. In this work, we investigate the design of SMAs offering a wider frequency range of operation than that offered by conventional designs. To achieve this goal, microphones are distributed both on and at a distance from the surface of a rigid spherical baffle. The contributions of the paper are as follows. First, we present a general framework for modeling SMAs whose sensors are located at different distances from the array center and calculating optimal filters for the decomposition of the sound field into spherical harmonic modes. Second, we present an optimization method to design multi-radius SMAs with an optimally wide frequency range of operation given the total number of sensors available and target spatial resolution. Lastly, based on the optimization results, we built a prototype dual-radius SMA with 64 microphones. We present measurement results for the prototype microphone array and compare these results with theory.
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