Results 1 to 10 of about 69,760 (269)

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

Journal of Inequalities and Applications, 2022
The coupled fractional Fourier transform F α , β $\mathcal {F}_{\alpha ,\beta}$ is a two-dimensional fractional Fourier transform depending on two angles α and β, which are coupled in such a way that the transform parameters are γ = ( α + β ) / 2 $\gamma
Firdous A. Shah, Waseem Z. Lone, Kottakkaran Sooppy Nisar, Thabet Abdeljawad   +3 more
doaj   +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 ...
Xiaoxiao Zeng, Kexin Fu, Xiaofei Li, Junjie Du, Weiran Fan   +4 more
doaj   +4 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.
Shraban Das, Kanailal Mahato, Ahmed I. Zayed   +2 more
doaj   +4 more sources

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

Matematički Vesnik, 2023
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
semanticscholar   +7 more sources

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

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, Negin Shariati, Mohammad-Ali Miri   +2 more
semanticscholar   +5 more sources

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.
Asma Elshamy, Zeinab S. I. Mansour, Ahmed Zayed   +2 more
doaj   +3 more sources

Uncertainty principles for coupled fractional Wigner–Ville distribution [PDF]

Royal Society Open Science
The coupled fractional Wigner–Ville distribution is a more general version of the fractional Wigner–Ville distribution. Main properties including boundedness, Moyal’s formula and inversion formula are studied in detail for the transformation ...
Andi Tenri Ajeng Nur, Mawardi Bahri, Nasrullah Bachtiar, Amran Rahim   +3 more
doaj   +3 more sources

Some Results on Pseudo-differential Operators Related Coupled Fractional Fourier Transform Involving Semi-norms & Norms

Asian Research Journal of Mathematics
In this manuscript, some results on the Pseudo-differential operators (p.d.o.) L(x, y,D′ x,y) and L(x, y,D′ x,y) are found by using semi-norms and norms in Herbitian Spaces, a set of compact operators and L2(R×R) with the symbol classes Λ(R × R × R × R).
Abhisekh Shekhar
semanticscholar   +3 more sources

The Estimation of Pseudo-differential Operators Utilising the Coupled Fractional Fourier Transform and a Certain Inequality

Asian Research Journal of Mathematics
In this research work, the symbol class Λ (R×R×R×R) is discussed. Then, we give the fundamental properties of this symbol class. Furthermore, the Pseudo-differential operators (p.d.o.) A(x, y,D′x,y) and A(x, y,D′x,y) involving the coupled fractional Fourier transform (CFrFT) Fα1,α2 associated with symbol classes are defined.
Abhisekh Shekhar
semanticscholar   +3 more sources

Compactness Properties of Pseudo-differential Operators Related with the Coupled Fractional Fourier Transform

Asian Research Journal of Mathematics
In this paper, we introduce the characterization of compactness of the coupled fractional Fourier transform (CFrFT). Few results on compactness of pseudo-differential operators (P.D.O) connected with CFrFT are investigated.
Abhisekh Shekhar
semanticscholar   +3 more sources