Related papers: Quaternion Linear Canonical Wavelet Transform and …
In this work, we use the concept of quaternion time and demonstrate that it can be applied for description of four-dimensional space-time intervals. We demonstrate that the quaternion time interval together with the finite speed of light…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
In this paper, we define new type of convolution and correlation theorems associated with the offset linear canonical transform (OLCT). Additionally, we discuss their applications in multiplicative filter design, which may prove useful in…
In this paper, we introduce and study the quadratic-phase Dunkl transform, a novel integral transform on the real line parameterized by five real numbers $(a, b, c, d, e)$ and a multiplicity parameter $\mu\geq -1/2$. We define the transform…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…
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…
The offset linear canonical transform (OLCT) provides a more general framework for a number of well known linear integral transforms in signal processing and optics, such as Fourier transform, fractional Fourier transform, linear canonical…
In this paper, we have given a new definition of continuous fractional wavelet transform in $\mathbb{R}^N$, namely the multidimensional fractional wavelet transform (MFrWT) and studied some of the basic properties along with the inner…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms…
This work undertakes a twofold investigation. In the first part, we examine the inequalities and uncertainty principles in the framework of offset linear canonical transform (OLCT), with particular attention to its scaling and shifting…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters…
We study a one-component quaternionic wave equation which is relativistically covariant. Bi-linear forms include a conserved 4-current and an antisymmetric second rank tensor. Waves propagate within the light-cone and there is a conserved…
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
The quaternion Fourier transform (QFT), a generalization of the classical 2D Fourier transform, plays an increasingly active role in particular signal and colour image processing. There tends to be an inordinate degree of interest placed on…
Quaternion models have been developed for both direction of arrival estimation and beamforming based on crossed-dipole arrays in the past. However, for almost all the models, especially for adaptive beamforming, the desired signal is still…