Abstract
The aim of this work is to construct the Ateb transforms based on Ateb-functions as a generalization of orthogonal Fourier transform. It was proved that these transforms satisfy the properties of linearity, symmetry and similarity. The Hartley transform is a real linear operator, and symmetric and self-inverse properties for Hartley Ateb-transform were proved. The one-dimensional discrete and two-dimensional discrete Ateb transforms were represented. Discrete transforms were used for construction digital watermark for the information security aim in the computer networks.
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Dronjuk, I., Nazarkevich, M. (2015). A Study on Ateb Transform as a Generalization of Fourier Transform. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_79
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DOI: https://doi.org/10.1007/978-3-319-12577-0_79
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-12576-3
Online ISBN: 978-3-319-12577-0
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