Related papers: Quaternion Linear Canonical Wavelet Transform and …
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be…
Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
The curvelet transform is a special type of wavelet transform, which is useful for estimating the locations and orientations of waves propagating in Euclidean space. We prove an uncertainty principle that lower-bounds the variance of these…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
For a two-dimensional canonical system $y'(t)=zJH(t)y(t)$ on the half-line $(0,\infty)$ whose Hamiltonian $H$ is a.e. positive semi-definite, denote by $q_H$ its Weyl coefficient. De Branges' inverse spectral theorem states that the…
Diverse applications in photonics and microwave engineering require a means of measurement of the instantaneous frequency of a signal. A photonic implementation typically applies an interferometer equipped with three or more output ports to…
We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The…
Some general remarks about integral transform approaches to response functions are made. Their advantage for calculating cross sections at energies in the continuum is stressed. In particular we discuss the class of kernels that allow…
We present an experiment demonstrating entanglement-enhanced classical communication capacity of a quantum channel with correlated noise. The channel is modelled by a fiber optic link exhibiting random birefringence that fluctuates on a…
A conjecture in quantum mechanics states that any quantum canonical transformation can decompose into a sequence of three basic canonical transformations; gauge, point and interchange of coordinates and momenta. It is shown that if one…
Vision transformer family has dominated the satellite pan-sharpening field driven by the global-wise spatial information modeling mechanism from the core self-attention ingredient. The standard modeling rules within these promising…
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…
Cavity-based quantum node is a competitive platform for distributed quantum networks. Here, we characterize a high-finesse Fabry-Perot optical resonator for coupling single or few atomic quantum registers. Our cavity consists of two mirrors…
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
Accurately calculating time delays between signals is pivotal in many modern physics applications. One approach to estimating these delays is computing the cross-spectrum in the time-frequency domain. Linear time-frequency representations,…
This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
The purpose of this paper is to represent the integral Hankel transform as a series. If one uses B-spline wavelet this series is a linear combination of the hypergeometrical functions. Numerical evaluation of the test function with known…