Fractional wavelet transform using an unbalanced lifting structure

Date
2011
Advisor
Instructor
Source Title
Proceedings of SPIE
Print ISSN
0277-786X
Electronic ISSN
Publisher
SPIE
Volume
8058
Issue
Pages
Language
English
Type
Conference Paper
Journal Title
Journal ISSN
Volume Title
Abstract

In this article, we introduce the concept of fractional wavelet transform. Using a two-channel unbalanced lifting structure it is possible to decompose a given discrete-time signal x[n] sampled with period T into two sub-signals x1[n] and x2[n] whose average sampling periods are pT and qT, respectively. Fractions p and q are rational numbers satisfying the condition: 1/p + 1/q = 1. The low-band sub-signal x 1[n] comes from [0, π/p] band and the high-band wavelet signal x 2[n] comes from (π/p, π] band of the original signal x[n]. Filters used in the liftingstructure are designed using the Lagrange interpolation formula. It is straightforward to extend the proposed fractional wavelet transform to two or higher dimensions in a separable or non separable manner. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

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Book Title
Keywords
Lifting, Discrete-time signals, Fractional wavelet transforms, Higher dimensions, Lagrange interpolations, Lifting, Lifting structure, Multirate signal processing, Original signal, Rational numbers, Sampling period, Two-channel, Biological systems, Neural networks, Signal processing, Wavelet transforms
Citation
Published Version (Please cite this version)