A framework for diffuseness evaluation using a tight-frame microphone array configuration

TL;DR

This work addresses robust spatial diffuseness evaluation across heterogeneous microphone arrays by introducing a velocity-only covariance framework that avoids mode whitening or spherical-harmonic decomposition. It compares three array designs (Afmt, Fibo64, TF24), highlighting that tight-frame sampling (TF24) approaches near-isotropic directional coverage with a compact form, while eigenvalue-based diffuseness measures (notably $\Psi_{ ext{COM}}$) offer stability across conditions. The study combines simulations with measured-experiment validation to show that velocity-based diffuseness indices track beam-to-diffuse energy ratios linearly and are less susceptible to interference artifacts than traditional intensity-based metrics. The framework thus enables robust, broadband, cross-array diffuseness characterization, with practical implications for spatial sound-field analysis and design of compact, reliable sensing systems.

Abstract

This work presents a unified framework for estimating both sound-field direction and diffuseness using practical microphone arrays with different spatial configurations. Building on covariance-based diffuseness models, we formulate a velocity-only covariance approach that enables consistent diffuseness evaluation across heterogeneous array geometries without requiring mode whitening or spherical-harmonic decomposition. Three array types -- an A-format array, a rigid-sphere array, and a newly proposed tight-frame array -- are modeled and compared through both simulations and measurement-based experiments. The results show that the tight-frame configuration achieves near-isotropic directional sampling and reproduces diffuseness characteristics comparable to those of higher-order spherical arrays, while maintaining a compact physical structure. We further examine the accuracy of direction-of-arrival estimation based on acoustic intensity within the same framework. These findings connect theoretical diffuseness analysis with implementable array designs and support the development of robust, broadband methods for spatial-sound-field characterization.

Figures (15)

• Figure 1: Coordinate system used in this study.
• Figure 2: Microphone arrangements used in this study. (a) Microphone arrangement modeled after the AMBEO VR Mic (A-format array). (b) Array model based on the Eigenmike, in which 64 omnidirectional microphones are uniformly distributed on a rigid-sphere baffle according to a Fibonacci lattice. (c) Proposed tight-frame microphone configuration, in which microphones are spaced every 45° in azimuth and ±45° in elevation.
• Figure 3: Schematic diagram of the signals used to construct the C-C method in the TF24 system. Twelve directional pairs are formed from 24 microphones.
• Figure 4: Measured (solid lines) and modeled (broken lines) directivities of the DPA2012 cardioid microphone assumed in the Afmt and the TF24 array. To avoid visual clutter, the polar plots show the responses for 250 Hz to 1 kHz on the left half and for 2 kHz to 8 kHz on the right half. In the calculations presented in the text, however, a wider frequency range from 63 Hz to 16 kHz was analyzed in octave bands.
• Figure 5: Representative example of modeled directional responses derived from the microphone directivity polynomial in Eq. (\ref{['eq:directivity_model']}) at 1 kHz. The results are shown (a) in linear magnitude and (b) in level (dB). The outer curve represents the pseudo-omnidirectional response obtained from the sum signal, whereas the inner curve corresponds to the pseudo-figure-of-eight response obtained from the difference signal. Both responses were derived from a pair of oppositely oriented microphones placed in the TF24 array with an inter-microphone spacing of 20 mm.