Browsing by Subject "Discrete-time signals"
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Item Unknown Directionally selective fractional wavelet transform using a 2-d non-separable unbalanced lifting structure(Springer, Berlin, Heidelberg, 2012) Keskin, Furkan; Çetin, A. EnisIn this paper, we extend the recently introduced concept of fractional wavelet transform to obtain directional subbands of an image. Fractional wavelet decomposition is based on two-channel unbalanced lifting structures whereby it is possible to decompose a given discrete-time signal x[n] sampled with period T into two sub-signals x 1[n] and x 2[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. Filters used in the lifting structure are designed using the Lagrange interpolation formula. 2-d separable and non-separable extensions of the proposed fractional wavelet transform are developed. Using a non-separable unbalanced lifting structure, directional subimages for five different directions are obtained. © 2012 Springer-Verlag.Item Open Access Fractional wavelet transform using an unbalanced lifting structure(SPIE, 2011) Habiboǧlu, Y. Hakan; Köse, Kıvanç; Çetin, A. EnisIn 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).