Jñānābha‎, Vol. 50 (1) (2020), 158-163

THE THEORETICAL OVERVIEW OF THE HARTLEY TRANSFORM AND THE GENERALIZED R-FUNCTION

By

Naseer Ahmad Malik

Department of Mathematics,

Government Postgraduate College for Women

Gandhi Nagar Jammu-180004 Jammu and Kashmir, India.

email: drnaseerulhassan@gmail.com

Farooq Ahmad

Department of Mathematics,

Government College for Women

Nawakadal-190001, Jammu and Kashmir, India.

email: sheikhfarooq85@gmail.com

D. K. Jain

Department of Mathematics,

Madhav Institute of Technology and Science,

Gwalior-474005, Madhya Pradash India.

email: jain dkj@yahoo.co.in

(Received : April 03, 2020 ; Revised: June 02, 2020)

Abstract

In this paper the R-functions have been mentioned in connection with integral operator named as Hartely transform. The Hartley transform is a mathematical transformation which is closely related to the better known Fourier transform. The properties that differentiate the Hartley Transform from its Fourier counterpart are that the forward and the inverse transforms are identical and also that the Hartley transform of a real signal is a real function of frequency. The Whitened Hartley spectrum, which stems from the Hartley transform, is a bounded function that encapsulates the phase content of a signal. The Whitened Hartley spectrum, unlike the Fourier phase spectrum, is a function that does not suffer from discontinuities or wrapping ambiguities. An overview on how the Whitened Hartley spectrum encapsulates the phase content of a signal more efficiently compared with its Fourier counterpart as well as the reason that phase unwrapping is not necessary for the

Whitened Hartley spectrum, are provided in this study. Moreover, in this study, we deal with the function which is significant generalization of Fox’s H-function which was introduced by Hartley and Lorenzo and later on modified by Jain et al.

2010 Mathematics Subject Classifications: 26A33, 33C05, 33C10, 33C20.

Keywords and phrases: Generalized fractional integral operators, H-Function, I-function and R-function.

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