Research Article
Haar Wavelet Expansions of Signals and their Applications in Image Processing
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 173 - Issue 9 |
| Published: Sep 2017 |
| Authors: Shyam Lal, K. K. Shukla, Sarika Keshri |
10.5120/ijca2017915317
|
Shyam Lal, K. K. Shukla, Sarika Keshri . Haar Wavelet Expansions of Signals and their Applications in Image Processing. International Journal of Computer Applications. 173, 9 (Sep 2017), 1-23. DOI=10.5120/ijca2017915317
@article{ 10.5120/ijca2017915317,
author = { Shyam Lal,K. K. Shukla,Sarika Keshri },
title = { Haar Wavelet Expansions of Signals and their Applications in Image Processing },
journal = { International Journal of Computer Applications },
year = { 2017 },
volume = { 173 },
number = { 9 },
pages = { 1-23 },
doi = { 10.5120/ijca2017915317 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2017
%A Shyam Lal
%A K. K. Shukla
%A Sarika Keshri
%T Haar Wavelet Expansions of Signals and their Applications in Image Processing%T
%J International Journal of Computer Applications
%V 173
%N 9
%P 1-23
%R 10.5120/ijca2017915317
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In this paper, double wavelet series of a signal f of two variables t1 and t2 using Haar Scaling function Φ(t1, t2) = φ(t1)φ(t2) and Haar Wavelet function Ψ(t1, t2) = ψ(t1) ψ(t2) has been introduced and it has been verified by a number of examples. Several properties of this signal and it’s image have been studied.The significient result of this paper are the decomposition and reconstruction of signals of a single variable t1 and signals of two variables t1and t2 using Haar Scaling signal as well as Haar Wavelets.
References
- Haar A., Zurtheorie der orthogonalen funktionen systeme, Math. Ann., Vol. 69, pp. 331-371, 1910.
- Tichmarsh.,E.C., The Theory of Functions, Second Edition, Oxford University Press, (1939).
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