# Logarithmic uncertainty principle, convolution theorem related to continuous fractional wavelet transform and its properties on a generalized Sobolev space
> Bahri M.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_85023749802
Jurnal / Konferensi: International Journal of Wavelets Multiresolution and Information Processing
Tahun terbit: 2017
DOI: https://doi.org/10.1142/S0219691317500503
ISSN: 02196913
Kuartil SJR: Q3
Citations: 14

## Authors
- Bahri M.

## Abstract
The continuous fractional wavelet transform (CFrWT) is a nontrivial generalization of the classical wavelet transform (WT) in the fractional Fourier transform (FrFT) domain. Firstly, the Riemann–Lebesgue lemma for the FrFT is derived, and secondly, the CFrWT in terms of the FrFT is introduced. Based on the CFrWT, a different proof of the inner product relation and the inversion formula of the CFrWT are provided. Thereafter, a logarithmic uncertainty relation for the CFrWT is investigated and the convolution theorem related to the CFrWT is established using the convolution of the FrFT. The CFrWT on a generalized Sobolev space is introduced and its important properties are presented.

## Keywords
- Mathematics
- Fractional Fourier transform
- Sobolev space
- Convolution (computer science)
- Mathematical analysis
- Fourier transform
- Pure mathematics
- Harmonic wavelet transform
- Wavelet transform
- Wavelet
- Discrete wavelet transform
- Fourier analysis
- Computer science
- Machine learning
- Artificial intelligence
- Artificial neural network

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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