Related papers: Aliasing Effects for Samples of Spin Random Fields…
In this paper, aliasing effects are investigated for random fields defined on the d-dimensional sphere and reconstructed from discrete samples. First, we introduce the concept of an aliasing function on the sphere. The aliasing function…
A practical constraint that comes in the way of spectrum estimation of a continuous time stationary stochastic process is the minimum separation between successively observed samples of the process. When the underlying process is not…
We study general models of random fields associated with non-local equations in time and space. We discuss the properties of the corresponding angular power spectrum and find asymptotic results in terms of random time changes.
This is a direct computation of the spectral representation of homogeneous spin-weighted spherical random fields with arbitrary integer spin. It generalises known results from Cosmology for the spin-2 Cosmic Microwave Background…
We observe the noise spectrum of electron spins in bulk GaAs by Faraday rotation noise spectroscopy. The experimental technique enables the undisturbed measurement of the electron spin dynamics in semiconductors. We measure exemplarily the…
We construct time dependent random fields on the sphere through coordinates change and subordination and we study the associated angular power spectrum. Some of this random fields arise naturally as solutions of partial differential…
Recent experiments show striking unexpected features when alternating square magnetic field pulses are applied to ferromagnetic samples: domains show area reduction and domains walls change their roughness. We explain these phenomena with a…
Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Lo\`{e}ve expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of…
Obtaining constraints from the largest scales of a galaxy survey is challenging due to the survey mask allowing only partial measurement of large angular modes. This scatters information from the harmonic-space 2-point function away from…
A signal space approach is presented to study the Nyquist sampling, number of degrees of freedom and reconstruction of an electromagnetic field under arbitrary scattering conditions. Conventional signal processing tools, such as the…
Regular sampling in the time domain results in aliasing in the frequency domain that complicates the accurate determination of the periods of astrophysical variables. We propose to actively break the regularity of this sampling by providing…
By Faraday-rotation fluctuation spectroscopy one measures the spin noise via Faraday-induced fluctuations of the polarization plane of a laser transmitting the sample. In the fist part of this paper, we present a theoretical model of recent…
We explain why aliasing can be detected in a generic temporally-sampled stationary signal process. We then define a concept of stationarity that makes sense for single waveforms. (This is done without assuming that the waveform is a sample…
In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the…
We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the…
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…
Network reconstruction of dynamical continuous-time (CT) systems is motivated by applications in many fields. Due to experimental limitations, especially in biology, data could be sampled at low frequencies, leading to significant…
The paper aims at removing the aliasing effects of the whole focal stack generated from a sparse-sampled {4D} light field, while keeping the consistency across all the focal layers. We first explore the structural characteristics embedded…
We investigate theoretically and experimentally fluctuations of high spin (F>1/2) beyond the linear response regime and demonstrate dramatic modifications of the spin noise spectra in the high power density probe field. Several effects…
We conduct a comprehensive study into the impact of pixelization on cosmic shear, uncovering several sources of bias in standard pseudo-$C_\ell$ estimators based on discrete catalogues. We derive models that can bring residual biases to the…