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

TL;DR

This study analyzes how signal quantization impacts the performance of first-order 1D differential microphone arrays, revealing that quantization mainly affects null depth and interference suppression without altering beampattern shape.

Contribution

The paper provides an analytical expression for quantized beamformed output and explores quantization effects on array performance measures, a novel focus for 1D-DMAs.

Findings

Beampattern shape remains invariant across quantization bits.

Quantization affects null depth (SDN), increasing with more bits.

Directivity factor and front-to-back ratio are unaffected by quantization.

Abstract

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 the 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 suppression depth at null points (SDN). Simulation results reveal that the beampattern shape remains structurally invariant across quantization bit depths, with quantization primarily affecting SDN. DF and FBR remain constant with the varying number of quantization bits. Additionally, SDN 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 SDN degrades as the null moves closer to the source look direction (0 degree), indicating reduced interference suppression.