arXiv subjects

Akira Omoto

Publications and source records attributed to Akira Omoto.

7 recordsLinked to original sources

arXiv2026

Broadband Acoustic Intensity Direction Estimation with Tight-Frame Cardioid Arrays

This study experimentally investigates source-direction estimation from acoustic intensity using paired cardioid microphones, with particular emphasis on well-balanced arrangements known as tight frames. Impulse responses were measured at 6 or 24 microphone positions, and two opposed-pair spacings were examined. The resulting arrays were evaluated for a single source, coherent interference between waves arriving from two orthogonal directions, and directional tracking in the presence of interfering waves from multiple directions. The results demonstrate broadband acoustic-intensity direction estimation from 50 Hz to 20 kHz, with the 24-microphone arrangement and the shorter spacing generally providing smaller errors.

eess.AS↗

arXiv2026

Acoustic intensity estimation using cardioid microphone pairs in tight-frame configurations

This paper investigates acoustic intensity estimation using pairs of cardioid microphones based on the cardioid-cardioid (C-C) method. Unlike conventional pressure-difference techniques, the C-C method is intrinsically less sensitive to the relationship between microphone spacing and acoustic wavelength. However, practical microphones inevitably deviate from ideal cardioid directivity, producing direction-dependent estimation errors. To improve robustness against such errors, a measurement framework based on spherical tight-frame microphone configurations is proposed. Directional intensity components measured along multiple axes are combined to reconstruct the three-dimensional acoustic intensity vector. Furthermore, directivity errors are represented using Legendre polynomial and spherical harmonic expansions, and a geometry-dependent leakage metric is introduced to quantify the error-suppression capability of different microphone arrangements. Theoretical analysis and numerical simulations demonstrate that tight-frame configurations effectively suppress direction-dependent errors through geometric averaging. The proposed leakage metric provides a qualitative indication of microphone directivity imperfections on the reconstructed intensity vector. The results further indicate that accurate wide-band acoustic-intensity estimation can be achieved even with relatively large microphone spacings, which are generally impractical in conventional pressure-difference approaches. The proposed framework provides a physically interpretable and practically useful approach for acoustic intensity measurement using directional microphone arrays.

eess.AS↗

arXiv2026

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

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.

eess.AS↗

arXiv2026

Directional reflection modeling via wavenumber-domain reflection coefficient for 3D acoustic field simulation

This study proposes a framework for incorporating wavenumber-domain acoustic reflection coefficients into sound field analysis to characterize direction-dependent material reflection and scattering phenomena. The reflection coefficient is defined as the amplitude ratio between incident and reflected waves for each propagation direction and is estimated from spatial Fourier transforms of the incident and reflected sound fields. The resulting wavenumber-domain reflection coefficients are converted into an acoustic admittance representation that is directly compatible with numerical methods such as the Boundary Element Method (BEM), enabling simulation of reflections beyond simple specular components. Unlike conventional extended reaction models, the proposed approach avoids explicit modeling of the material interior. This significantly reduces computational cost while allowing direct use of measured data, empirical models, or user-defined directional reflection characteristics. The validity of the proposed formulation was previously demonstrated by the authors through two-dimensional sound field simulations, in which accurate reproduction of direction-dependent reflection behavior was confirmed. In the present work, the framework is extended to three-dimensional analysis, demonstrating its applicability to more realistic and complex acoustic environments. The proposed approach provides a practical and flexible tool for simulating direction-dependent acoustic reflections and scattering, with potential applications in architectural acoustics, material characterization, and noise control.

eess.AS↗

arXiv2025

Beamforming in the Reproducing Kernel Domain Based on Spatial Differentiation

This paper proposes a novel beamforming framework in the reproducing kernel domain, derived from a unified interpretation of directional response as spatial differentiation of the sound field. By representing directional response using polynomial differential operators, the proposed method enables the formulation of arbitrary beam patterns including non-axisymmetric. The derivation of the reproducing kernel associated with the interior fields is mathematically supported by Hobson's theorem, which allows concise analytical expressions. Furthermore, the proposed framework generalizes conventional spherical harmonic domain beamformers by reinterpreting them as spatial differential operators, thereby clarifying their theoretical structure and extensibility. Three numerical simulations conducted in two-dimensional space confirm the validity of the method.

eess.AS↗

arXiv2024

Polar Coordinate Solutions of the Helmholtz Equation in General Dimensions and an Orthonormal Basis

In acoustical engineering, analytical methodologies are often restricted to two or three dimensions; however, a general-dimensional approach can enhance learning and implementation efficiency while providing a unified understanding of foundational principles. In this manuscript, we present a straightforward derivation of the polar coordinate solutions of the homogeneous Helmholtz equation in general dimensions. We define the radial function as a special function, with coefficients selected to maintain orthonormality within a reproducing kernel Hilbert space, which simplifies its kernel representation. Additionally, we derive an orthonormal basis for this space, thereby demonstrating that the addition theorem arises naturally from a property of the reproducing kernel.

math.GM↗

arXiv2024

Frequency-Domain Sound Field from the Perspective of Band-Limited Functions

In this paper, the frequency-domain sound field is regarded as an element of some band-limited function space, and a representation of the field as a linear combination of the reproducing kernel in that space is proposed. This model has the strongest representational capacity of all function systems when we know only the sound pressure information at arbitrary positions. The proposed model can be considered a generalization of the existing three-dimensional sound field model using the reproducing kernel of the solution space of the Helmholtz equation to the spatial dimension. One of the advantages of capturing the frequency-domain sound field in this way is the simplicity achieved for the estimation formula of the wavenumber spectrum. Two numerical simulations were conducted to validate the proposed methods.

cs.SD↗