IJPAM: Volume 21, No. 1 (2005)

WAVELETS IN A FINITE DIMENSIONAL
VECTOR SPACE AND DECOMPOSITION OF A SIGNAL

G.V. Deepa$^1$, R. Radha$^2$
$^1$Department of Mathematics
Anna University (C.E.G.)
Chennai, 600 025, INDIA
e-mail: gv_deepa81@yahoo.com
$^2$Department of Mathematics
Indian Institute of Technology
Madras, Chennai, 600 036, INDIA
e-mail: radharam@iitm.ac.in


Abstract.Wavelets in the vector space $V=[F_p(\sqrt{2}, \sqrt{m})]^N$ over the field $F=F_p(\sqrt{2}, \sqrt{m})$, where $p$ is an odd prime and $N \equiv m(\text{\rm mod} ~ p)$ is constructed. This is used in expressing $V$ as a direct sum of subspaces $V_j's$ based on the scales. An algorithm in decomposing a signal at various resolutions is also provided. The algorithm is implemented using MATLAB and its application in power engineering is mentioned.

Received: March 29, 2005

AMS Subject Classification: 42C40, 12E20

Key Words and Phrases: Fourier transforms, finite fields, multi resolution, quadratic residue, wavelets

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 1