相关论文: Aliasing effects for random fields over spheres of…
We present a rigorous analytical method for harmonic analysis of the angular error of rotary and linear encoders with sine/cosine output signals in quadrature that are distorted by superimposed Fourier series. To calculate the angle from…
In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation,…
Spatial aliasing affects spaced microphone arrays, causing directional ambiguity above certain frequencies, degrading spatial and spectral accuracy of beamformers. Given the limitations of conventional signal processing and the scarcity of…
One of the key approximations to range simulation is downscaling the image, dictated by the natural trigonometric relationships that arise due to long-distance viewing. It is well-known that standard downsampling applied to an image without…
Pseudoscalar particles, with almost zero mass and very weak coupling to the visible matter, arise in many extensions of the standard model of particle physics. Their mixing with photons in the presence of an external magnetic field leads to…
Based on the Fourier extension, we propose an oversampling collocation method for solving the elliptic partial differential equations with variable coefficients over arbitrary irregular domains. This method only uses the function values on…
Imaging devices exploit the Nyquist-Shannon sampling theorem to avoid both aliasing and redundant oversampling by design. Conversely, in medical image resampling, images are considered as continuous functions, are warped by a spatial…
We perform a duality transformation that allows one to express the partition function of the d-dimensional Ising model with random nearest neighbor coupling in terms of new spin variables defined on the square plaquettes of the lattice. The…
We use the techniques developed in [1] to study the local average of random fields with spectral density $1/f^{\alpha}$. We study their scaling properties and show that the self-similarity of $1/f$ random fields is preserved under the local…
We study the regularity properties of Gaussian fields defined over spheres cross time. In particular, we consider two alternative spectral decompositions for a Gaussian field on $\mathbb{S}^d \times \mathbb{R}$. For each decomposition, we…
We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are…
We establish sensitivity analysis on the sphere. We present formulas that allow us to decompose a function $f\colon \mathbb S^d\rightarrow \mathbb R$ into a sum of terms $f_{\boldsymbol u,\boldsymbol \xi}$. The index $\boldsymbol u$ is a…
Efficient estimators of Fourier-space statistics for large number of objects rely on Fast Fourier Transforms (FFTs), which are affected by aliasing from unresolved small scale modes due to the finite FFT grid. Aliasing takes the form of a…
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…
It is commonplace in cosmology to analyze fields projected onto the celestial sphere, and in particular density fields that are defined by a set of points e.g. galaxies. When performing an harmonic-space analysis of such data (e.g. an…
We show that a class of de Branges spaces, generated by means of generalized Fourier transforms associated with perturbed Bessel differential equations, has the properties of oversampling and aliasing.
We provide a method for fast and exact simulation of Gaussian random fields on spheres having isotropic covariance functions. The method proposed is then extended to Gaussian random fields defined over spheres cross time and having…
This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for…
Neural vocoders often struggle with aliasing in latent feature spaces, caused by time-domain nonlinear operations and resampling layers. Aliasing folds high-frequency components into the low-frequency range, making aliased and original…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…