Spatial sigma-delta modulation for coarsely quantized linear, circular, and spherical arrays

Abstract

Quantization noise shaping, also known as sigma-delta modulation, is widely used in analog-to-digital converters. Such converters oversample a signal in time, quantize it to one or a few bits of precision, and then use analog feedback to shape quantization noise outside the band of interest, producing a high-precision output. Similarly, if a sensor array is spatially oversampled so that its elements are much less than one-half wavelength apart, then quantization noise can be propagated between channels to shape its spatial distribution. A beamformer acts as a spatial filter, removing shaped quantization noise to produce a high-precision output even with coarsely quantized sensors. Spatial sigma-delta modulation has been explored primarily for radio-frequency applications using linear arrays. In this presentation, we apply spatial noise shaping to dense acoustic sensor arrays, including circular and spherical arrays. For immersive audio applications, we demonstrate how noise-shaping feedback can be used to push quantization noise into higher-order Ambisonic modes.