Analysis of Null Related Beampattern Measures and Signal Quantization Effects for Linear Differential Microphone Arrays

A differential microphone array (DMA) offers enhanced capabilities to obtain sharp nulls at the cost of relatively broad peaks in the beam power pattern. This can be used for applications that require nullification or attenuation of interfering sources. To the best of our knowledge, the existing literature lacks measures that directly assess the efficacy of nulls, and null-related measures have not been investigated in the context of differential microphone arrays (DMAs). This paper offers new insights about the utility of DMAs by proposing measures that characterize the nulls in their beam power patterns. We investigate the performance of differential beamformers by presenting and evaluating null-related measures namely null depth (ND) and Null Width (NW) as a function of depth level relative to the beam power pattern maxima. A study of signal quantization effects due to data acquisition for 1st, 2nd and 3rd order linear DMAs and for different beampatterns i.e. dipole, cardioid, hypercardioid and supercardioid is presented. An analytical expression for the quantized beamformed output for any general $ N^{th} $ order DMA is formulated. Simulation results of the variation of ND with number of quantization bits and the variation of NW as a function of depth are also presented and inferences are drawn. Lab experiments are conducted in a fully anechoic room to support the simulation results. The measured beampattern exhibits a pronounced null depth, confirming the effectiveness of the experimental setup.

Effect of Signal Quantization on Performance Measures of a 1st Order One Dimensional Differential Microphone Array

In practical systems, recorded analog signals must be digitized for processing, introducing quantization as a critical aspect of data acquisition. While prior studies have examined quantization effects in various signal processing contexts, its impact on differential microphone arrays (DMAs), particularly in one-dimensional (1D) first-order configurations, remains unexplored. This paper investigates the influence of signal quantization on performance of first-order 1D DMAs across various beampatterns. An analytical expression for quantized beamformed output for a first-order 1D DMA has been formulated. The effect of signal quantization has been studied on array performance measures such as the Beampattern, Directivity Factor (DF), Front-to-Back Ratio (FBR), and null depth (ND). Simulation results reveal that beampattern shape remains structurally invariant across quantization bit depths, with quantization primarily affecting ND. DF and FBR remain constant with the varying number of quantization bits. Additionally, ND is shown to be frequency-independent; however, it increases with increasing quantization bit depths, enhancing interference suppression. The study also examines the effect of steering nulls across the azimuthal range, showing that ND degrades as the null moves closer to the source look direction, indicating reduced interference suppression.