Abstract
This paper gives a simple and straightforward method for designing spline based biorthogonal wavelets. Biorthogonal wavelets differ from orthogonal wavelets in that the former has more flexibility in its design. This is because, they enable the design of wavelets which are symmetric and smooth, which is not possible in the case of orthogonal wavelets (except Haar wavelet). However, the compromise made to achieve the symmetry property is that the non-zero coefficients in the analysis and synthesis filters are not the same for biorthogonal wavelets. The existing algorithm for spline biorthogonal wavelet design involves complex formulas, whose proof is also not easily understandable. In this paper, we present a very simple way of constructing spline based biorthogonal wavelets, which results in the same nonzero coefficients for the analysis and synthesis filters.
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References
Herley, C., Vetterli, M.: Wavelets and Recursive Filter Banks. IEEE Transactions on Signal Processing 41(8) (August 1993)
Butzer, P.L., Fischer, A., Ruckforth, K.: Scaling functions and wavelets with vanishing moments. Computers & Mathematics with Applications 27(3), 33–39 (1994)
Olsen, L., Samavati, F.F., Bartels, R.H.: Multiresolution B-Splines based on Wavelet Constraints. In: Eurographics Symposium on Geometry Processing, pp. 1–10 (2005)
Godavarthy, S.: Generating Spline Wavelets. In: Proceedings of the 36th Annual Southeast Regional Conference, pp. 8–14 (1998) ISBN: 1–58113-030-9
Soman, K.P., Ramachandran, K.I.: Insight into wavelets – From theory to Practice, 2nd edn. PHI (2005)
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Arathi, T., Soman, K.P., Parameshwaran, L. (2010). Spline Biorthogonal Wavelet Design. In: Das, V.V., Vijaykumar, R. (eds) Information and Communication Technologies. ICT 2010. Communications in Computer and Information Science, vol 101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15766-0_118
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DOI: https://doi.org/10.1007/978-3-642-15766-0_118
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15765-3
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