Open AccessModified Fourier transform and its properties
Author(s) -
Dawood Khan,
Abdul Rehman,
Saleem Iqbal,
Ali Ahmed,
Sana Jafar,
Maria Baloch
Publication year - 2021
Publication title -
mathematica montisnigri
Language(s) - English
Resource type - Journals
eISSN - 2704-4963
pISSN - 0354-2238
DOI - 10.20948/mathmontis-2021-51-5
Subject(s) - fourier transform , fourier transform on finite groups , fourier inversion theorem , mathematics , abelian group , discrete time fourier transform , convolution (computer science) , fractional fourier transform , harmonic wavelet transform , maxima and minima , mathematical analysis , discrete fourier transform (general) , short time fourier transform , pure mathematics , fourier analysis , computer science , wavelet transform , wavelet , artificial intelligence , discrete wavelet transform , artificial neural network
In this manuscript we recommend a new description of the modified Fourier transform for a function which is absolutely integrable, having finite number of maxima and minima and finite number of discontinuities which further takes the form of simple Fourier transform for substituting α = e where α > 0 and α ≠ 1. Moreover we prove various results of the modified Fourier transform and also we show that the set that consists of whole modified Fourier transformable functions under the convolution operation is a commutative semi group as well as form an abelian group under the operation of addition