Theoretical and Numerical Evaluation of Sensitivity, SNR and Received RMS Error of A Telescopic Microphone System by Using A Spherical Array

Abstract

This paper newly proposes a telescopic microphone system that may establish the high sensitivity and SNR, and narrow directivity in 3D-space, by using passive dynamic focusing and spherical wave synthesis with a spherical sensor array. On this system, passive dynamic focusing and spherical wave synthesis are realized by compensating the amplitude attenuation of detected signals, due to wave propagation, with variable gain elements, adjusting the relative time delays among the signals with variable delay elements, so as to match the resultant signals with those propagated hypothetically from the source at a predetermined focused point, and summing up the resultant signals. As the result, the sensitivity of the system is enhanced, for a sound source at the focused point, by a multiplicative factor of the number of used microphones. For uncorrelated additive detection noises, the SNR of the system output is improved, for the source at the focused point, approximately by the same factor as the sensitivity. After the sensitivity 3D-distribution of the system and the SNR characteristics of a synthesized output being made clear, the relative RMS error spatial distribution of the system output is examined through computer simulations by assuming a FM wide-band source signal which covers audio frequency bands. All the results of theoretical or numerical analysis and computer simulations illustrate the effectiveness as well as the fundamental characteristics of the proposed telescopic microphone system, resulting in the possibility of constructing the intended telescopic microphone system.