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, Kivanc Kose, 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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