相关论文: A Function Based on Chebyshev Polynomials as an Al…

This paper proposes a novel, rigorous and simple Fourier-transformation approach to study resonances in a perfectly conducting slab with finite number of subwavelength slits of width $h\ll 1$. Since regions outside the slits are variable…

We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev…

There is presented an approach to find an approximation polynomial of a function with two variables based on the two dimensional discrete Fourier transform. The approximation polynomial is expressed through Chebyshev polynomials. There is…

In this paper we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) and the fast sinc transform as its application. The computation of NNFFT is mainly based on the nonuniform fast Fourier…

We present a new method for proving Correa-Jofr\'e-Thibault theorem that monotonicity of subdifferential implies convexity of the function. This new method is based on barrier functions. Barrier functions help overcome some of the main…

A point spread function of hexagonally segmented telescopes is derived by a new symmetrical formulation. By introducing three variables on a pupil plane, the Fourier transform of pupil functions is derived by a three-dimensional Fourier…

A low-profile, modified Complementary Frequency Selective Surface (CFSS) with dual band-pass characteristic is presented. This technique adds independent control of the operation bands, which was a limitation from previous FSSs design based…

We have developed a photonic filter featuring dual independently tunable passbands. Employing the reconstruction equivalent-chirp technique, we designed linearly chirped sampled Bragg gratings with two equivalent phase shifts positioned at…

In this letter, we present a fast and well-conditioned spectral method based on the Chebyshev polynomials for computing the continuous part of the nonlinear Fourier spectrum. The algorithm achieves a complexity of $O(N_{\text{iter.}}N\log…

Graph filters are crucial tools in processing the spectrum of graph signals. In this paper, we propose to design universal IIR graph filters with low computational complexity by using three kinds of functions, which are Butterworth,…

This article introduces the Generalized Fourier Series (GFS), a novel spectral method that extends the clas- sical Fourier series to non-periodic functions. GFS addresses key challenges such as the Gibbs phenomenon and poor convergence in…

Motivated by constraints on the dark energy equation of state from supernova-data, we propose a formalism for the Bayesian inference of functions: Starting at a functional variant of the Kullback-Leibler divergence we construct a functional…

We derive closed-form expressions for the poles and zeros of approximate fractional integrator/differentiator filters, which correspond to spectral roll-off filters having any desired log-log slope to a controllable degree of accuracy over…

In a recent paper, I. Selesnick and C.S. Burrus developed a design method for maximally flat FIR low-pass digital filters with reduced group delay. Their approach leads to a system of polynomial equations depending on three integer design…

Spectral methods are renowned for their high accuracy and efficiency in solving partial differential equations. The Fourier pseudo-spectral method is limited to periodic domains and suffers from Gibbs oscillations in non-periodic problems.…

A variety of techniques have been developed for the approximation of non-periodic functions. In particular, there are approximation techniques based on rank-$1$ lattices and transformed rank-$1$ lattices, including methods that use sampling…

The least squares based eigenfilter method has been applied to the design of both finite impulse response (FIR) filters and wideband beamformers successfully. It involves calculating the resultant filter coefficients as the eigenvector of…

The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…

This paper deals with some special integral transforms of Bargmann-Fock type in the setting of quaternionic valued slice hyperholomorphic and Cauchy-Fueter regular functions. The construction is based on the well-known Fueter mapping…

A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…