# A comparative study on properties and uncertainty principles of fractional Fourier transform and offset fractional Fourier transform
> Bahri M.

URL kanonis: https://discover.unhas.ac.id/publications/a-comparative-study-on-properties-and-uncertainty-principles-of-fractional-fouri
Jurnal / Konferensi: Results in Applied Mathematics
Tahun terbit: 2025
DOI: https://doi.org/10.1016/j.rinam.2025.100616
Kuartil SJR: Q3
Citations: 1

## Authors
- Bahri M.

## Abstract
This work deals with the offset fractional Fourier transform (OFrFT), which is a more general version of the fractional Fourier transform (FrFT). We demonstrate the basic properties such as translation, modulation and parity. The results are generalization of the FrFT properties. We study a relation of the OFrFT with the FrFT and the Fourier transform. Based on the relation, the key properties such as Parseval’s identity and inversion formula are derived. Applying the properties and the relation allow us to establish several versions of the uncertainty inequalities for the OFrFT. In addition, we discuss the comparison of the OFrFT with the FrFT in terms of properties and uncertainty principles. Finally, we perform an illustrative example to demonstrate that the value of Heisenberg uncertainty inequality for the OFrFT is bigger than that of Heisenberg uncertainty inequality for the FrFT and effect of the offset parameter in minimizing the Heisenberg uncertainty principle associated with the OFrFT.

## Keywords
- Fractional Fourier transform
- Mathematics
- Fourier transform
- Uncertainty principle
- Offset (computer science)
- Applied mathematics
- Mathematical analysis
- Inversion (geology)
- Discrete-time Fourier transform
- Non-uniform discrete Fourier transform
- Generalization
- Discrete Fourier transform (general)
- Relation (database)
- Fourier analysis
- Harmonic wavelet transform
- Short-time Fourier transform
- Algorithm

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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