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      • Department of Electrical and Electronics Engineering
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      Fractional wavelet transform using an unbalanced lifting structure

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      Author
      Habiboǧlu, Y. Hakan
      Köse, Kıvanç
      Çetin, A. Enis
      Date
      2011
      Source Title
      Proceedings of SPIE
      Print ISSN
      0277-786X
      Publisher
      SPIE
      Volume
      8058
      Language
      English
      Type
      Conference Paper
      Item Usage Stats
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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
      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
      Permalink
      http://hdl.handle.net/11693/28344
      Published Version (Please cite this version)
      http://dx.doi.org/10.1117/12.882408
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      • Department of Electrical and Electronics Engineering 3524
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