Fractional wavelet transform using an unbalanced lifting structure
Author
Habiboǧlu, Y. Hakan
Köse, Kıvanç
Çetin, A. Enis
Date
2011Source Title
Proceedings of SPIE
Print ISSN
0277-786X
Publisher
SPIE
Volume
8058
Language
English
Type
Conference PaperItem Usage Stats
142
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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).
Keywords
LiftingDiscrete-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