# Continuous quaternion fourier and wavelet transforms
> Bahri M.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_84906303591
Jurnal / Konferensi: International Journal of Wavelets Multiresolution and Information Processing
Tahun terbit: 2014
DOI: https://doi.org/10.1142/S0219691314600030
ISSN: 02196913
Kuartil SJR: Q3
Citations: 37

## Authors
- Bahri M.

## Abstract
A two-dimensional (2D) quaternion Fourier transform (QFT) defined with the kernel [Formula: see text] is proposed. Some fundamental properties, such as convolution, Plancherel and vector differential theorems, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.

## Keywords
- Quaternion
- Mathematics
- Quaternion algebra
- Algebra over a field
- Convolution (computer science)
- Fourier transform
- Kernel (algebra)
- Mathematical analysis
- Convolution theorem
- Pure mathematics
- Fractional Fourier transform
- Fourier analysis
- Computer science
- Artificial intelligence
- Geometry
- Algebra representation
- Cellular algebra
- Artificial neural network

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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