Related papers: On the Clifford short-time Fourier transform and i…
Classical Clifford theory studies the decomposition of simple $G$-modules into simple $H$-modules for some normal subgroup $H \triangleleft G$. In this paper we deal with chains of normal subgroups $1 \triangleleft G_1 \triangleleft \cdots…
We study the fractal uncertainty principle in the joint time-frequency representation, and we prove a version for the Short-Time Fourier transform with Gaussian window on the modulation spaces. This can equivalently be formulated in terms…
In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal and…
The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative viewpoint; the Fourier transform can be uniquely characterized…
In this paper, we study a few versions of the uncertainty principle for the short-time Fourier transform on the lattice $\mathbb Z^n \times \mathbb T^n$. In particular, we establish the uncertainty principle for orthonormal sequences,…
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…
Classical and recent results on uncertainty principles for functions on finite Abelian groups relate the cardinality of the support of a function to the cardinality of the support of its Fourier transforms. We use these results and their…
Inspired by the success of recent data augmentation methods for signals which act on time-frequency representations, we introduce an operator which convolves the short-time Fourier transform of a signal with a specified kernel. Analytical…
In this paper, some important properties of the windowed offset linear canonical transform (WOLCT) such as shift, modulation and orthogonality relation are introduced. Based on these properties we derive the convolution and correlation…
We extend the notion of Clifford index to reduced curves with planar singularities by considering rank 1 torsion free sheaves. We investigate the behaviour of the Clifford index with respect to the combinatorial properties of the curve and…
The offset linear canonical transform encompassing the numerous integral transforms, is a promising tool for analyzing non-stationary signals with more degrees of freedom. In this paper, we generalize the windowed offset linear canonical…
In this short note, we merge the areas of hypercomplex algebras with that of fractal interpolation and approximation. The outcome is a new holistic methodology that allows the modelling of phenomena exhibiting a complex self-referential…
This article studies the Fourier spectrum characterization of functions in the Clifford algebra-valued Hardy spaces $H^p(\mathbf R^{n+1}_+), 1\leq p\leq \infty.$ Namely, for $f\in L^p(\mathbf R^n)$, Clifford algebra-valued, $f$ is further…
A set of two-parameter bi-orthogonal eigen-spinors has been constructed from a deformed pseudo- Hermitian extension of Pauli Hamiltonian and its Hermitian conjugate. The Hamiltonians thus obtained are iso-spectral to the original Pauli…
Let $G$ be a locally compact Abelian group with a fixed Haar measure and, denote by $\widehat{G}$ its dual group. In this article, the authors obtain various boundedness of the short-time Fourier transform on Lorentz spaces:…
The quantized canonical space-time coordinates of a relativistic point particle are expressed in terms of the elements of a complex Clifford algebra which combines the complex properties of SL(2.C) and quantum mechanics. When the quantum…
This paper introduces and studies the basic properties of Clifford algebra valued conditional measures.
In this paper, we develop a new method based on the Laplace transform to study the Clifford-Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is obtained. When the dimension is even, the inverse…
We introduce the Non-commutative Subset Convolution - a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of…
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,…