相关论文: Nonlinear Spectral Characterization of Discrete Da…

Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…

Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…

The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this…

X-ray scattering patterns from emerging single particle experiments have commonly many missing or contaminated pixels. This complicates different analyses including projections on Fourier or other basis functions (for noise suppression,…

We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…

By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear…

A five-dimensional symmetry algebra consisting of Lie point symmetries is firstly computed for the nonlinear Schroedinger equation, which, together with a reflection invariance, generates two five-parameter solution groups. Three ansaetze…

We study a stochastic Nonlinear Schroedinger Equation (NLSE), with additive white Gaussian noise, by means of the Nonlinear Fourier Transform (NFT). In particular, we focus on the propagation of discrete eigenvalues along a focusing fiber.…

This paper explores the innovative application of the Fractional Fourier Transform (FrFT) in sound synthesis, highlighting its potential to redefine time-frequency analysis in audio processing. As an extension of the classical Fourier…

We investigate discretizations of the integrable discrete nonlinear Schr\"odinger dynamical system and related symplectic structures. We develop an effective scheme of invariant reducing the corresponding infinite system of ordinary…

Random non-linear Fourier features have recently shown remarkable performance in a wide-range of regression and classification applications. Motivated by this success, this article focuses on a sparse non-linear Fourier feature (NFF) model.…

Nonlinear interferometers allow for mid-infrared spectroscopy with near-infrared detection using correlated photons. Previous implementations have demonstrated a spectral resolution limited by spectrally selective detection. In our work, we…

The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…

We examine a recently-proposed family of nonlinear Schr\"odinger equations [J. Phys. A: Math. Gen. 27:1771(1994)] with respect to a group of transformations that linearize a subfamily of them. We investigate the structure of the whole…

We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…

The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier…

The Fourier spectrum is a family of dimensions that interpolates between the Fourier and Hausdorff dimensions and are defined in terms of certain energies which capture Fourier decay. In this paper we obtain a convenient discrete…

Linear theory for phonon scattering by discrete breathers in the discrete nonlinear Schroedinger equation using the transfer matrix approach is presented. Transmission and reflection coefficients are obtained as a function of the wave…

The Discrete Fourier Transform (DFT) is a fundamental computational primitive, and the fastest known algorithm for computing the DFT is the FFT (Fast Fourier Transform) algorithm. One remarkable feature of FFT is the fact that its runtime…

This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…