Constructive Approaches to Biorthogonal Finitely Supported Ternary Wavelets and Wavelet Wraps


Article Preview

In this paper, the notion of biorthogonal two-directional shortly supported wavelets with poly-scale is developed. A new method for designing two-directional biorthogonal wavelets is proposed. The existence of shortly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A novel constructive method for designing a sort of biorthogonal vector-valued wavelet wraps is presented and their biorthogonality traits are characerized. Two biorthogonality formulas regarding these wavelet wraps are established.



Advanced Materials Research (Volumes 219-220)

Edited by:

Helen Zhang, Gang Shen and David Jin






J. T. Zhao and H. L. Guo, "Constructive Approaches to Biorthogonal Finitely Supported Ternary Wavelets and Wavelet Wraps", Advanced Materials Research, Vols. 219-220, pp. 504-507, 2011

Online since:

March 2011




[1] Yang S. and Cheng Z, Wang H. Construction of biorthogonal multiwavelets, J. Math. Anal. Appl., Vol. 276, No. 1, pp.1-12, (2002).

[2] H. He and S. Cheng. Home network power-line communiction signal processing based on wavelet packet analysis, . IEEE Trans. Power Delivery, 20 (3) : pp.1879-1885 , (2005).

DOI: 10.1109/tpwrd.2004.843489

[3] Kaneko H., Noren D. R. and Novaprateep B. Wavelet applications to the Petrov-Galerkin method for Hammrstein equations, J. Appl. Numer. Math., Vol. 45, No. 2, pp.255-273, (2003).

DOI: 10.1016/s0168-9274(02)00173-3

[4] Chen Q. and Cheng Z. A study on compactly supported orthogonal vector-valued wavelets and wavlet packets,. Chaos, Solitons & Fractals, Vol. 31, No. 4, pp.1024-1034, (2007).

DOI: 10.1016/j.chaos.2006.03.097

[5] Fowler J. E. and Li H . Wavelet Transforms for Vector Fields Using Omnidirectionally Balanced Multiwavelets, IEEE Trans. Signal Processing, Vol. 50, No. 10, pp.3018-3027, (2002).

DOI: 10.1109/tsp.2002.805488

[6] Hardin D. P. and Marasovich J. A., Biorthogonal multiwavelets on [-1, 1] , Appl. Comput. Harmon. Anal. Vol. 7, No. 1, pp.34-51, (1999).

[7] Chen Q. and Huo A. The research of a class of biorthogonal compactly supported vector-valued wavelets. 2009, 41(2): 951–961.

DOI: 10.1016/j.chaos.2008.04.025

[8] Han J. and Chen Q. Characterization of a class of orthogonal multiple vector-valued wavelet pa- ckets. International Journal of wavelets, multiresolution and information processing, 2008, 6 (4): 631-641.

In order to see related information, you need to Login.