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A Study on B-Spline Wavelets and Wavelet Packets

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In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline wavelet packets are also investigated.
Cite this paper
Khan, S. and Ahmad, M. (2014) A Study on B-Spline Wavelets and Wavelet Packets. Applied Mathematics, 5, 3001-3010. doi: 10.4236/am.2014.519287. 

[1] Chui, C.K. and Wang, J.Z. (1992) On Compactly Supported Spline Wavelets and a Duality Principle. Transactions of the American Mathematical Society, 330, 903-915.
http://dx.doi.org/10.1090/S0002-9947-1992-1076613-3
[2] Battle, G.A. (1987) A Block Spin Construction of Ondelettes, Part-I: Lemarié Functions. Communications in Mathematical Physics, 110, 610-615.
http://dx.doi.org/10.1007/BF01205550
[3] Lemarié, P.G. (1988) Ondelettes á localisation exponentielles, Journal de Mathématiques Pures et Appliquées, 67, 227-236.
[4] Chui, C.K. and Wang, J.Z. (1991) A Cardinal Spline Approach to Wavelets. Proceedings of the American Mathematical Society, 113, 785-793.
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[5] Chui, C.K. and Wang, J.Z. (1992) A General Framework of Compactly Supported Splines and Wavelets. Journal of Approximation Theory, 71, 263-304.
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[6] Coifman, R.R., Meyer, Y. and Wickerhauser, M.V. (1992) Wavelet Analysis and Signal Processing. In: Ruskai, M.B., et al., Eds., Wavelets and Their Applications, Jones and Barlett, Boston, 153-178.
[7] Coifman, R.R., Meyer, Y. and Wickerhauser, M.V. (1992) Size Properties of Wavelet Packets. In: Ruskai, M.B., et al., Eds., Wavelets and Their Applications, Jones and Barlett, Boston, 453-547.
[8] Chui, C.K. and Li, C. (1993) Nonorthogonal Wavelet Packets. SIAM Journal on Mathematical Analysis, 24, 712-738.
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[9] Yang, S. and Cheng, Z. (2000) A Scale Multiple Orthogonal Wavelet Packets. Mathematica Applicata, in Chinese, 13, 61-65.
[10] Xia, X.G. and Suter, B.W. (1996) Vector Valued Wavelets and Vector Filter Banks. IEEE Transactions on Signal Processing, 44, 508-518.
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[11] Chen, Q. and Cheng, Z. (2007) A Study on Compactly Supported Orthogonal Vector Valued Wavelets and Wavelet Packets. Chaos, Solitons and Fractals, 31, 1024-1034.
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