# Fractional fourier transform: A variant of Heisenberg uncertainty principle, weighted uncertainty inequality and application
> Bahri M.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_105047460409
Jurnal / Konferensi: International Journal of Optimization and Control Theories and Applications
Tahun terbit: 2026
DOI: https://doi.org/10.36922/IJOCTA026190077
ISSN: 21460957
Kuartil SJR: Q2
Citations: 1

## Authors
- Bahri M.

## Abstract
The focus of this article is to propose two different versions of the Heisenberg uncertainty principle related to the fractional Fourier transform (FrFT). The first version is directly derived using the basic connection between the traditional Fourier transform (FT) and the FrFT, and the second is derived by exploiting time differentiation property and Parseval’s formula for the FrFT. In addition, a weighted uncertainty inequality related to this transformation is investigated. As a simple illustration of the use of the obtained results, we design the fractional characteristic function. An inequality describing the relation between the probability density function and its fractional characteristic function is presented.

## Keywords
- Mathematics
- Uncertainty principle
- Fourier transform
- Property (philosophy)
- Characteristic function (probability theory)
- Transformation (genetics)
- Fractional Fourier transform
- Applied mathematics
- Function (biology)
- Focus (optics)
- Probability density function
- Simple (philosophy)
- Mathematical analysis
- Fourier analysis
- Fractional calculus
- Calculus (dental)
- Fourier series
- Connection (principal bundle)
- Inequality
- Probability theory
- Relation (database)
- Discrete Fourier transform (general)
- Type (biology)
- Fourier inversion theorem

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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