NDLI: Three Dimensional Fractional Fourier-Mellin Transform, and its Applications

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Three Dimensional Fractional Fourier-Mellin Transform, and its Applications

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Three Dimensional Fractional Fourier-Mellin Transform, and its Applications

Content Provider	Horizon Research Publishing Corporation
Author	Sinha, Arvind Kumar Panda, Srikumar
Abstract	The main objective of the paper is to study the three-dimensional fractional Fourier Mellin transforms (3DFRFMT), their basic properties and applicability due to mainly use in the radar system, reconstruction of grayscale images, in the detection of the human face, etc. Only the fractional Fourier transform is based on time-frequency distribution, whereas only the fractional Mellin transform is on scale covariant transformation. Both transforms can discover action in the definite assortment. The fractional Fourier transform is applicable for controlling the range of shift, whereas the fractional Mellin transform is accustomed to managing the range of rotation and scaling of the function. So, combining both transformations, we get an elegant expression for 3DFRFMT, which can be used in several fields. The paper introduces the concept of three-dimensional fractional Fourier Mellin transforms and their applications. Modulation property is the most useful concept in the signal system, radar technology, pattern reorganization, and many more in the integral transform. Parseval's identity applies to the conservation of energy in the universe. Thus we establish the modulation theorem, Parseval's theorem, scaling theorem, analytic theorem for three-dimensional fractional Fourier Mellin transform. We also give some examples of three-dimensional fractional Fourier-Mellin transform on some functions. Finally, we provide three-dimensional fractional Fourier-Mellin transform applications for solving homogeneous and non-homogeneous Mboctara partial differential equations that we can apply with advantages to solve the different types of problems in signal processing systems. The transform is beneficial in a maritime strategy as a co-realtor to control moments in any specific three-dimensional space. The concept is the most powerful tool to deal with any information system problems. After obtaining the generalization, we can explore many more ideas in applying three-dimensional fractional Fourier-Mellin transformations in many real word problems.
Ending Page	480
Page Count	16
Starting Page	465
File Format	PDF
ISSN	23322071
e-ISSN	23322144
DOI	10.13189/ms.2021.090407
Alternate Webpage(s)	https://www.hrpub.org/journals/article_info.php?aid=10999
Journal	Mathematics and Statistics
Issue Number	4
Volume Number	9
Language	English
Publisher	Horizon Research Publishing
Publisher Date	2021-07-01
Access Restriction	Open
Subject Keyword	Fractional Fourier Transform Fractional Mellin Transform Three Dimensional Fractional Fourier-mellin Transform Test Function
Content Type	Text
Resource Type	Article
Subject	Economics and Econometrics Statistics, Probability and Uncertainty Statistics and Probability

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Mellin Transform of an Exponential Fourier Transform Expressed in Terms of the Lerch Function

ANALYTICITY OF TWO DIMENSIONAL FRACTIONAL FOURIER-MELLIN TRANSFORM

On a Fractional Master Equation and a Fractional Diffusion Equation

Solution of One –dimensional Fractional Diffusion Equations Involving Caputo Fractional Derivatives in terms of the Mittag - Leffler Functions

MODULATION AND PARSEVAL’S THEOREM FOR DISTRIBUTIONAL TWO DIMENSIONAL FOURIER-MELLIN TRANSFORM

Applications of Two Dimensional Fractional Mellin Transform

Applications of Two Dimensional Fractional Fourier-Mellin Transform to Differential Equations

ANALYTICITY OF TWO DIMENSIONAL FRACTIONAL FOURIER-MELLIN TRANSFORM

Topological Propertiesof Two Dimensional Fractional Fourier-mellin Transform

Three Dimensional Fractional Fourier-Mellin Transform, and its Applications

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