Related papers: Linear Canonical Jacobi-Dunkl Transform: Theory an…
The aim of this paper is to establish and study the linear canonical Dunkl wavelet transform. We begin by introducing the generalized translation operator and generalized convolution product for the linear canonical Dunkl transform and we…
The polar wavelet transform (PWT) has been proven to be a powerful mathematical tool for signal and image processing in recent years. Due to the increasing demand for directional representations of signals in engineering, it is impossible…
Linear canonical transforms (LCTs) are of importance in many areas of science and engineering with many applications. Therefore a satisfactory discrete implementation is of considerable interest. Although there are methods that link the…
Linear Canonical Transformations (LCTs) are known in signal processing and optics as the generalization of certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the…
We define a novel time-frequency analyzing tool, namely linear canonical wavelet transform (LCWT) and study some of its important properties like inner product relation, reconstruction formula and also characterize its range. We obtain…
The linear canonical transform (LCT) serves as a powerful generalization of the Fourier transform (FT), encapsulating various integral transforms within a unified framework. This versatility has made it a cornerstone in fields such as…
Generalized analytic signal associated with the linear canonical transform (LCT) was proposed recently by Fu and Li ["Generalized Analytic Signal Associated With Linear Canonical Transform," Opt. Commun., vol. 281, pp. 1468-1472, 2008].…
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
In this paper, we introduce the notion of windowed linear canonical transform in biquaternion setting namely Biquaternion Windowed Linear Canonical Transform (BiQWLCT) and various properties of BiQWLCT, such as linearity, shift, parity,…
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…
We investigate the 2D quaternion windowed linear canonical transform(QWLCT) in this paper. Firstly, we propose the new definition of the QWLCT, and then several important properties of newly defined QWLCT, such as bounded, shift,…
In this article, we undertake a two-fold investigation. First, we establish Calderons reproducing formula for the linear canonical Dunkl continuous wavelet transform. Further, we define the reproducing kernel linear canonical Dunkl Sobolev…
We investigate two methods of constructing a solution of the Schr\"{o}dinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schr\"{o}dinger equation from linear…
We both review and augment the lightcone conformal truncation (LCT) method. LCT is a Hamiltonian truncation method for calculating dynamical quantities in QFT in infinite volume. This document is a self-contained, pedagogical introduction…
The linear canonical transform (LCT) has attained respectable status within a short span and is being broadly employed across several disciplines of science and engineering including signal processing, optical and radar systems, electrical…
Canonical transformations using the idea of quantum generating functions are applied to construct a quantum Hamilton-Jacobi theory, based on the analogy with the classical case. An operator and a c-number forms of the time-dependent quantum…
We contend that what are called Linear Canonical Transforms (LCTs) should be seen as a part of the theory of unitary irreducible representations of the '2+1' Lorentz group. The integral kernel representation found by Collins, Moshinsky and…
In this article, we give a new definition of the linear canonical Stockwell transform (LCST) and study its basic properties along with the inner product relation, reconstruction formula and also characterize the range of the transform and…
A GBDT version of the B\"acklund-Darboux transformation for a non-isospectral canonical system is considered. Applications to multiplicative integrals and their limit values, to characteristic matrix functions and to linear similarity…
This work is devoted to the development of the octonion linear canonical transform (OLCT) theory proposed by Gao and Li in 2021 that has been designated as an emerging tool in the scenario of signal processing. The purpose of this work is…