The octonionic Fourier transform: Uncertainty relations and convolution

The uncertainty principle is a fundamental principle in mathematics and physics, and also plays an important role in signal processing. On the other side, the octonion Fourier transform has got a lot of attentions in recent years. It is the aim of this paper to establish various uncertainty relation...

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Bibliographic Details
Published in:Signal processing 2019-11, Vol.164, p.295-300
Main Author: Lian, Pan
Format: Article
Language:English
Subjects:
Convolution
Fourier transform
Octonion
Quaternion
Uncertainty principle
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Summary:The uncertainty principle is a fundamental principle in mathematics and physics, and also plays an important role in signal processing. On the other side, the octonion Fourier transform has got a lot of attentions in recent years. It is the aim of this paper to establish various uncertainty relations for this new hyper-complex Fourier transform. Based on the relations between the octonion Fourier transform and the quaternion Fourier transform, several uncertainty inequalities are derived neatly, including the logarithmic uncertainty inequality, local uncertainty inequalities, generalized global uncertainty inequality and the Benedicks–Amrein–Berthier inequality. In addition, the Mustard convolution associated to the octonion Fourier transform is discussed as well.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2019.06.015