Related papers: Visualization of Linear Operations in the Spherica…
The objective of this paper is to characterize harmonic Hardy spaces and a boundary behavior of harmonic functions on a smooth domain in real Euclidean space.
Performing linear operations using optical devices is a crucial building block in many fields ranging from telecommunication to optical analogue computation and machine learning. For many of these applications, key requirements are…
Spherical microphone arrays have been recently studied for spatial sound recording, speech communication, and sound field analysis for room acoustics and noise control. Complementary theoretical studies presented progress in spatial…
We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…
Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…
Synthetic aperture sonar (SAS) reconstruction requires recovering both the spatial distribution of acoustic scatterers and their direction-dependent response. Time-domain backprojection is the most common 3D SAS reconstruction algorithm,…
Spatial audio formats like Ambisonics are playback device layout-agnostic and well-suited for applications such as teleconferencing and virtual reality. Conventional Ambisonic encoding methods often rely on spherical microphone arrays for…
This paper presents a new approach for tackling the shift-invariance problem in the discrete Haar domain, without trading off any of its desirable properties, such as compression, separability, orthogonality, and symmetry. The paper…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
Spatial sound field interpolation relies on suitable models to both conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest…
Matrix elements of spinor and principal series representations of the Lorentz group are studied in the basis of complex angular momentum (helicity basis). It is shown that matrix elements are expressed via hyperspherical functions…
We present a new representation of harmonic sounds that linearizes the dynamics of pitch and spectral envelope, while remaining stable to deformations in the time-frequency plane. It is an instance of the scattering transform, a generic…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs.…
Ambisonics is an established framework to capture, process, and reproduce spatial sound fields based on its spherical harmonics representation. We propose a generalization of conventional spherical ambisonics to the spheroidal coordinate…
In the current method for the sound field translation tasks based on spherical harmonic (SH) analysis, the solution based on the additive theorem usually faces the problem of singular values caused by large matrix condition numbers. The…
Holographic multiple-input multiple-output (H-MIMO) systems represent a paradigm shift in wireless communications by enabling quasi-continuous apertures. Unlike conventional MIMO systems, H-MIMO with subwavelength antenna spacing operates…
Spectral analysis of open surfaces is gaining momentum for studying surface morphology in engineering, computer graphics, and medical domains. This analysis is enabled using proper parameterization approaches on the target analysis domain.…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…