Continuous wavelet transform on local fields
Ashish Pathak
TL;DR
This paper introduces the continuous wavelet transform on local fields, defining the mother wavelet and exploring fundamental properties like inversion, Parseval relation, and convolution within this mathematical framework.
Contribution
It extends the theory of continuous wavelet transforms to local fields, providing foundational definitions and properties for this mathematical setting.
Findings
Defined the mother wavelet on local fields
Derived the inversion formula for CWT on local fields
Established the Parseval relation and convolution properties
Abstract
The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution are also studied.
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Taxonomy
TopicsImage and Signal Denoising Methods · Seismic Imaging and Inversion Techniques · Mathematical Analysis and Transform Methods