Related papers: Biquaternion Z Transform
The z-transform of a sequence is a classical tool used within signal processing, control theory, computer science, and electrical engineering. It allows for studying sequences from their generating functions, with many operations that can…
Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented.
Nowadays, we have seen that dual quaternion algorithms are used in 3D coordinate transformation problems due to their advantages. 3D coordinate transformation problem is one of the important problems in geodesy. This transformation problem…
Transformations in the field of computer graphics and geometry are one of the most important concepts for efficient manipulation and control of objects in 2-dimensional and 3-dimensional space. Transformations take many forms each with…
A nonhomogeneous system of linear recurrence equations can be recognized by an automaton $\mathcal{A}$ over a one-letter alphabet $A = \{z\}$. Conversely, the automaton $\mathcal{A}$ generates precisely this nonhomogeneous system of linear…
In this paper, we describe the structural properties of the cone of $\mathcal{Z}$-transformations on the second order cone in terms of the semidefinite cone and copositive/completely positive cones induced by the second order cone and its…
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…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
The Z Transform is a mathematical operation in signal processing, which gives a tractable way to solve linear, constant-coefficient difference equations. Based on the classical Z transform and inspired by the thought of sliding DFT, a new…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
Over the past few years, the applications of dual-quaternions have not only developed in many different directions but has also evolved in exciting ways in several areas. As dual-quaternions offer an efficient and compact symbolic form with…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
We give an alternative method to obtain normal forms of reversible equivariant vector fields. We adapt the classical method using tools from invariant theory to establish formulae that take symmetries into account as a starting point.…
A triangulation is called $z$-knotted if it has a single zigzag (up to reversing). A $z$-orientation on a triangulation is a minimal collection of zigzags which double covers the set of edges. An edge is of type I if zigzags from the…
Recent layout-to-image models have achieved remarkable progress in spatial controllability. However, they still struggle with inter-object occlusion. When bounding boxes overlap, most existing methods lack explicit occlusion information,…
In this paper, we investigate bi-periodic Padovan and bi-periodic Perrin quaternions over the quaternion algebra Q_Zp. We introduce the bi-periodic Perrin sequence and clarify its structural relationship with the bi-periodic Padovan…
The paper presents some new results on Z-related sets obtained by computational methods. We give a complete enumeration of all Z-related sets in $\mathbb{Z}_{N}$ for small $N$. Furthermore, we establish that there is a reasonable…
The algebra B of bicomplex numbers is viewed as a complexification of the Archimedean f-algebra of hyperbolic numbers D. This lattice-theoretic approach allows us to establish new properties of the so-called D-norms. In particular, we show…
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,…
Baxter permutations are known to be in bijection with a wide number of combinatorial objects. Previously, it was shown that each of these objects had a natural involution which was carried equivariantly by the known bijections, and the…