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All Journal Journal of the Indonesian Mathematical Society Hilbert Journal of Mathematical Analysis
Mawardi Bahri
Hasanuddin University
Chemistry Control & Systems Engineering Engineering Mathematics Physics

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Journal : Hilbert Journal of Mathematical Analysis

 1 
A useful inequality for quaternion linear canonical transform Bahri, Mawardi
Hilbert Journal of Mathematical Analysis Vol. 1 No. 1 (2022): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v1i1.7

Abstract

In this work, we first introduce the quaternion Fourier transform. We explore its relation to the quaternion linear Fourier transform and utilize this fact to extend an inequality for the quaternion Fourier transform in the framework of the quaternion linear canonical transform.
Three inequalities for quadratic-phase Fourier transform Bahri, Mawardi
Hilbert Journal of Mathematical Analysis Vol. 2 No. 1 (2023): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v2i1.18

Abstract

In this work, we introduce the one-dimensional quadratic-phase Fourier transform. The relation between one-dimensional quadratic-phase Fourier transform and one-dimensional Fourier transform is discussed in detail. We finally propose several versions of the inequalites related to one-dimensional quadratic-phase Fourier transform.
Simplified computation of useful functions in linear canonical transform Bahri, Mawardi
Hilbert Journal of Mathematical Analysis Vol. 3 No. 2 (2025): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i2.40

Abstract

The linear canonical transform is an extension of the usual Fourier transform because the Fourier transform is a special form of the linear canonical transform. It also is a valuable tool in signal analysis. Many essential properties of the Fourier transform can be transferred in the linear canonical Fourier domain with some changes. In this research paper, we first introduce the interesting connection between the linear canonical transform and Fourier transform. It is shown that the relation can be developed to efficiently evaluate Gaussian function in the linear canonical transform domain. Some examples of the Gaussian function in the linear canonical domain are also presented to illustrate the result.
Co-Authors Ryuichi Ashino Vaillancourt, Rémi