3 June 2011 Fractional wavelet transform using an unbalanced lifting structure
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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 x1[n] comes from [0, π/p] band and the high-band wavelet signal x2[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.
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Y. Hakan Habiboğlu, Y. Hakan Habiboğlu, Kivanc Kose, Kivanc Kose, A. Enis Çetin, A. Enis Çetin, } "Fractional wavelet transform using an unbalanced lifting structure", Proc. SPIE 8058, Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering IX, 805805 (3 June 2011); doi: 10.1117/12.882408; https://doi.org/10.1117/12.882408
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