Related papers: Optimal Fourier filtering of a function that is st…

We demonstrate that an aperiodic array of certain quantum networks comprising magnetic and non-magnetic atoms can act as perfect spin filters for particles with arbitrary spin state. This can be achieved by introducing minimal quasi-one…

Radio interferometers consisting of identical antennas arranged on a regular lattice permit fast Fourier transform beamforming, which reduces the correlation cost from $\mathcal{O}(n^2)$ in the number of antennas to $\mathcal{O}(n\log n)$.…

Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-known Radon transform and the cumulative density transform,…

We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…

This paper deals with the optimal synthesis of aperture fields for (radiating) near-field communications in obstructed environments. A physically consistent model based on knife-edge diffraction is used to formulate the problem as a…

In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse…

Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…

The Fraunhofer diffraction of quantum particles from materials with sharp electron-density edges or symmetric bond structures is ubiquitous. In contrast, diffraction from atoms with characteristic asymptotically-diffused electron…

We present an open geometry Fourier modal method based on a new combination of open boundary conditions and an efficient $k$-space discretization. The open boundary of the computational domain is obtained using basis functions that expand…

We use a microwave cavity to investigate the influence of a movable absorbing center on the wave function of an open quantum dot. Our study shows that the absorber acts as a position-selective probe, which may be used to suppress those wave…

We have employed Particle Swarm Optimization to address a stochastic variant of the Smallest Enclosing Sphere estimation problem. An efficient algorithm has been developed to ascertain the optimal center and radius of a sphere encompassing…

We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…

The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear…

In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…

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…

The problem of computing the Fourier Transform of a signal whose spectrum is dominated by a small number $k$ of frequencies quickly and using a small number of samples of the signal in time domain (the Sparse FFT problem) has received…

A new scheme for constructing approximate effective electron potentials within density-functional theory is proposed. The scheme consists of calculating the effective potential for a series of reference systems, and then using these…

The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth…

A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspects: (i) the proposed particle filter is a controlled…

We generalize the technique of fringe-rate filtering, whereby visibilities measured by a radio interferometer are re-weighted according to their temporal variation. As the Earth rotates, radio sources traverse through an interferometer's…