Journal
SIGNAL PROCESSING
Volume 86, Issue 9, Pages 2340-2350Publisher
ELSEVIER
DOI: 10.1016/j.sigpro.2005.10.017
Keywords
fractional generalized splines; symmetrical functions; fractional wavelet transform; interpolation; approximation
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This paper presents the concept of fractional generalized splines, which is an extension of the idea of Unser's fractional splines. The first part of this paper describes a method for construction of fractional generalized splines through evaluating fractional finite differences. The main key to our approach is to provide an additional tuning parameter 'alpha' by using a generating function, which is the solution of the Laguerre's nth-order differential equation. The second part of the paper deals with characterization of these functions in both time and frequency domain and shows how to use these results for construction of wavelet bases in L-2 for signal processing applications. This paper also present simulation results to reveal the suitability of the proposed basis functions for signal approximation. (c) 2005 Elsevier B.V. All rights reserved.
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