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Two-Dimensional Discrete Coupled Fractional Fourier Transform (DCFrFT)

Fractal and Fractional
The fractional Fourier transform is critical in signal processing and supports many applications. Signal processing is one notable application. Implementing the fractional Fourier transform requires discrete versions. As a result, defining a discrete coupled fractional Fourier transform (DCFrFT) is essential.
Zeinab Mansour, Ahmed Zayed
exaly   +6 more sources

Characterization of Pseudo-Differential Operators Associated with the Coupled Fractional Fourier Transform

Axioms
The main aim of this article is to derive certain continuity and boundedness properties of the coupled fractional Fourier transform on Schwartz-like spaces. We extend the domain of the coupled fractional Fourier transform to the space of tempered distributions and then study the mapping properties of pseudo-differential operators associated with the ...
Kanailal Mahato, Ahmed Zayed
exaly   +7 more sources

On the class of uncertainty inequalities for the coupled fractional Fourier transform [PDF]

Journal of Inequalities and Applications, 2022
AbstractThe coupled fractional Fourier transform$\mathcal {F}_{\alpha ,\beta}$Fα,βis a two-dimensional fractional Fourier transform depending on two anglesαandβ, which are coupled in such a way that the transform parameters are$\gamma =(\alpha +\beta )/2$γ=(α+β)/2and$\delta =(\alpha -\beta )/2$δ=(α−β)/2.
Kottakkaran Sooppy Nisar, Firdous A Shāh, Thabet Abdeljawad   +2 more
exaly   +4 more sources

Numerical Method for Multi-Dimensional Coupled Forward-Backward Stochastic Differential Equations Based on Fractional Fourier Fast Transform [PDF]

Fractal and Fractional, 2023
Forward-backward stochastic differential equations (FBSDEs) have received more and more attention in the past two decades. FBSDEs can be applied to many fields, such as economics and finance, engineering control, population dynamics analysis, and so on.
Xiaofei Li
exaly   +5 more sources

Real-Time Discrete Fractional Fourier Transform Using Metamaterial Coupled Lines Network

IEEE Transactions on Microwave Theory and Techniques, 2023
Discrete Fractional Fourier Transforms (DFrFT) are universal mathematical tools in signal processing, communications and microwave sensing. Despite the excessive applications of DFrFT, implementation of corresponding fractional orders in the baseband signal often leads to bulky, power-hungry, and high-latency systems.
Rasool Keshavarz, Mohammad-Ali Miri, Negin Shariati   +2 more
exaly   +5 more sources

Convolution and Correlation Forms for the Offset Coupled Fractional Fourier Transform [PDF]

Jurnal MSA ( Matematika dan Statistika serta Aplikasinya)
This work presents convolution and correlation in  offset coupled fractional Fourier transform. The offset coupled fractional Fourier transform can be regarded as a generalized version of the coupled fractional Fourier transform. Various properties including this work like inversion formula and Parseval are studied in general and in detail for the ...
Nasrullah, Wahyuni Ekasasmita, Nurwahidah   +2 more
core   +4 more sources

SHARP HAUSDORFF YOUNG INEQUALITY AND INVERSION FORMULA FOR THE COUPLED WINDOWED OFFSET FRACTIONAL FOURIER TRANSFORM

Jurnal Matematika UNAND
This work presents the Sharp Hausdorff-Young inequality for the Coupled windowed offset fractional Fourier transform. The coupled windowed offset fractional Fourier transform can be regarded as a generalized version of the fractional windowed Fourier transform.
Nasrullah Bachtiar, Erica Grace Simanjuntak, Nora Madonna   +2 more
core   +4 more sources

Coupled Fractional Fourier Transform: Properties and Uncertainty Principle

Journal of the Indonesian Mathematical Society
The coupled fractional Fourier transform is a general form of the fractional Fourier transform. In the present work, we demonstrate basic properties of the proposed transformation, such as linearity, shifting and modulation. We also propose convolution and correlation theorems and then explore a generalized uncertainty principle for the coupled ...
Mawardi Bahri
openalex   +3 more sources

UNCERTAINTY PRINCIPLES ASSOCIATED WITH THE SHORT TIME QUATERNION COUPLED FRACTIONAL FOURIER TRANSFORM [PDF]

Matematički Vesnik
In this paper, we extend the coupled fractional Fourier transform of a complex valued functions to that of the quaternion valued functions on $\mathbb{R}^4$ and call it the quaternion coupled fractional Fourier transform (QCFrFT). We obtain the sharp Hausdorff-Young inequality for QCFrFT and obtain the associated Rènyi uncertainty principle.
Gupta, Bivek, Verma, Amit K., Agarwal, Ravi P.   +2 more
openalex   +3 more sources

Product and Commutator of pseudo-differential operators involving the coupled fractional Fourier transform

International Journal of Applied Mathematics
The symbol class Λ(R × R × R × R) is discussed and it is shownthat the product of any two symbols from this class is again in Λ. The Pseudodifferential operators (p.d.o.) A(x, y,Dx0,y) and A (x, y,Dx0,y) involving the coupledfractional Fourier transform Fα1,α2associated with symbol classes are defined.Product and Commutator for the p.d.o.
Abhisekh Shekhar
openalex   +3 more sources