# Some properties of windowed linear canonical transform and its logarithmic uncertainty principle
> Bahri M.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_84979493796
Jurnal / Konferensi: International Journal of Wavelets Multiresolution and Information Processing
Tahun terbit: 2016
DOI: https://doi.org/10.1142/S0219691316500156
ISSN: 02196913
Kuartil SJR: Q3
Citations: 62

## Authors
- Bahri M.

## Abstract
Based on the relationship between the Fourier transform (FT) and linear canonical transform (LCT), a logarithmic uncertainty principle and Hausdorff–Young inequality in the LCT domains are derived. In order to construct the windowed linear canonical transform (WLCT), Gabor filters associated with the LCT is introduced. Using the basic connection between the classical windowed Fourier transform (WFT) and the WLCT, a new proof of inversion formula for the WLCT is provided. This relation allows us to derive Lieb’s uncertainty principle associated with the WLCT. Some useful properties of the WLCT such as bounded, shift, modulation, switching, orthogonality relation, and characterization of range are also investigated in detail. By the Heisenberg uncertainty principle for the LCT and the orthogonality relation property for the WLCT, the Heisenberg uncertainty principle for the WLCT is established. This uncertainty principle gives information how a complex function and its WLCT relate. Lastly, the logarithmic uncertainty principle associated with the WLCT is obtained.

## Keywords
- Uncertainty principle
- Mathematics
- Fourier transform
- Orthogonality
- Logarithm
- Mathematical analysis
- Bounded function
- Applied mathematics
- Quantum mechanics
- Quantum
- Physics
- Geometry

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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