Related papers: Linear canonical wavelet transform and the associa…
The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…
Using Pathak and Pathak techniques, the basic function $D^\alpha(u,v,w)$ associated with general novel fractional wavelet transform (GNFrWT)is defined and its properties are investigated. By using basic function $D^\alpha(u,v,w)$…
The dual-tree complex wavelet transform (DT-CWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-CWT which, among other things, offers a…
We present a theory for wave scintillation in the situation with a time-dependent partially coherent source and a time-dependent randomly heterogeneous medium. Our objective is to understand how the scintillation index of the measured…
We present perturbation theory based on the inverse scattering transform method for solitons described by an equation with the inverse linear dispersion law $\omega\sim 1/k$, where $\omega$ is the frequency and $k$ is the wave number, and…
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…
This work considers uncertainty relations on time frequency distributions from a signal processing viewpoint. An uncertainty relation on the marginalizable time frequency distributions is given. A result from quantum mechanics is used on…
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In…
We consider the time dependent Maxwell system in the sense of distributions in the context of temporal interfaces. Just as with spatial interfaces, electromagnetic waves at temporal interfaces scatter and create a transmitted and reflected…
Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in…
The time-energy uncertainty relation is discussed for a relativistic massless particle. The Lorentz-invariant uncertainty relation is obtained between the root-mean-square energy deviation and the scatter of registration time. The…
A non-decimated wavelet transform (NDWT) is a popular version of wavelet transforms because of its many advantages in applications. The inherent redundancy of this transform proved beneficial in tasks of signal denoising and scaling…
The most recent generalization of octonion Fourier transform (OFT) is the octonion linear canonical transform (OLCT) that has become popular in present era due to its applications in color image and signal processing. On the other hand the…
A direct numerical simulation of an oblique shock wave impinging on a turbulent boundary layer at Mach number 2.28 is carried out at moderate Reynolds number, simulating flow conditions similar to those of the experiment by Dupont et al.…
We analyze a homogenization limit for the linear wave equation of second order. The spatial operator is assumed to be of divergence form with an oscillatory coefficient matrix $a^\varepsilon$ that is periodic with characteristic length…
We develop a unified theory for clocks and gravimeters using the interferences of multiple atomic waves put in levitation by traveling light pulses. Inspired by optical methods, we exhibit a propagation invariant, which enables to derive…
The propagation of acoustic waves in a poro-elastic medium of infinite extension containing spherical cavities randomly distributed is investigated. The scattering coefficients are computed in the low frequency limit using the sealed pore…
We study the process of dispersion of low-regularity solutions to the Schr\"odinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound…
In this paper, we introduce a new wavelet tool for studying the degree of non-periodicity of time series that is based on some recently defined tools, such as the \textit{windowed scalogram} and the \textit{scale index}. It is especially…
We introduce the joint time-frequency scattering transform, a time shift invariant descriptor of time-frequency structure for audio classification. It is obtained by applying a two-dimensional wavelet transform in time and log-frequency to…