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Piecewise‐quadratic Harmut basis functions and their application to problems in digital signal processing
Author(s) -
Singh Dhananjay,
Zaynidinov Hakimjon,
Lee HoonJae
Publication year - 2010
Publication title -
international journal of communication systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.344
H-Index - 49
eISSN - 1099-1131
pISSN - 1074-5351
DOI - 10.1002/dac.1093
Subject(s) - piecewise , computer science , basis (linear algebra) , quadratic equation , transformation (genetics) , basis function , constant (computer programming) , discontinuity (linguistics) , convergence (economics) , graphics , algorithm , quadratic programming , mathematical optimization , mathematics , computer graphics (images) , mathematical analysis , biochemistry , chemistry , geometry , economics , gene , programming language , economic growth
In this work, the well‐known system of orthogonal piecewise‐constant Harmut basis functions is investigated. As a result of research, their shortcomings are revealed such as weak convergence, discontinuity and others. To eliminate these problems, a new basis of piecewise‐quadratic Harmut functions is proposed and a fast spectral transformation algorithm is developed in this basis. For examples of analytically set and experimentally verified dependencies, the advantages of the algorithm for spectral transformations in a basis of piecewise‐quadratic Harmut functions are demonstrated. The proposed system and algorithm could find wide application in such areas as computer graphics, image processing and restoration, machine vision and multimedia, animation and programming of computer games. Copyright © 2010 John Wiley & Sons, Ltd.