Related papers: Visualization of Linear Operations in the Spherica…
The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation…
The present document reviews the mathematics behind binaural rendering of sound fields that are available as spherical harmonic expansion coefficients. This process is also known as binaural ambisonic decoding. We highlight that the details…
Ambisonics, a popular format of spatial audio, is the spherical harmonic (SH) representation of the plane wave density function of a sound field. Many algorithms operate in the SH domain and utilize the Ambisonics as their input signal. The…
Acoustical signal processing of directional representations of sound fields, including source, receiver, and scatterer transfer functions, are often expressed and modeled in the spherical harmonic domain (SHD). Certain such modeling…
Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a…
The objective of polarization rendering is to simulate the interaction of light with materials exhibiting polarization-dependent behavior. However, integrating polarization into rendering is challenging and increases computational costs…
We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional…
Utilizing spherical harmonic (SH) domain has been established as the default method of obtaining continuity over space in head-related transfer functions (HRTFs). This paper concerns different variants of extending this solution by…
Linear optical operations are fundamental and significant for both quantum mechanics and classical technologies. We demonstrate a non-cascaded approach to perform arbitrary unitary and non-unitary linear operations for N-dimensional…
The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties,…
Multi-channel speech enhancement utilizes spatial information from multiple microphones to extract the target speech. However, most existing methods do not explicitly model spatial cues, instead relying on implicit learning from…
This paper examines filtering on a sphere, by first examining the roles of spherical harmonic magnitude and phase. We show that phase is more important than magnitude in determining the structure of a spherical function. We examine the…
Characterizing sound field diffuseness has many practical applications, from room acoustics analysis to speech enhancement and sound field reproduction. In this paper we investigate how spherical microphone arrays (SMAs) can be used to…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
Spatial light modulators are versatile devices employed in a vast range of applications to modify the transverse phase or amplitude profile of an incident light beam. Most experiments are designed to use a specific polarization which…
In the last decade diffusion MRI has become a powerful tool to non-invasively study white-matter integrity in the brain. Recently many research groups have focused their attention on multi-shell spherical acquisitions with the aim of…
We present spatial-Slepian transform~(SST) for the representation of signals on the sphere to support localized signal analysis. We use well-optimally concentrated Slepian functions, obtained by solving the Slepian spatial-spectral…
Decomposing the domain of a function into parts has many uses in mathematics. A domain may naturally be a union of pieces, a function may be defined by cases, or different boundary conditions may hold on different regions. For any…
This work presents a theoretical formalism and the corresponding numerical techniques to obtain the approximation of fractional-order operators over a 1D domain via the smoothed particle hydrodynamics (SPH) method. The method is presented…