Orthogonal Wavelet Packets in Discrete Periodic Spaces and applications

Meixiang Yang

Abstract


This paper proposes the construction and application of orthogonal wavelet packets in discrete space $\ell^{2}(Z_{N})$. First, we give the definition and construction of orthogonal wavelet packets. Moreover, the corresponding orthogonal decomposition is proved. Then, the realization of decomposition and reconstruction algorithm is studied. Finally, a numerical example for signal processing is given, which shows that signal processing based on wavelet packets in discrete spaces can gain better effect in some cases.

Keywords


Orthogonal basis; Wavelet packets; Decomposition algorithm; Reconstruction algorithm

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References


R. Coiffman, Y. Meyer and S.Q. Quake, Signal processing and compression with wavelet packets, in Proceedings of the conference on wavelets, Marseilles, Springer, 1991.

M. W. Frazier, An introduction to wavelets through linear algebra, New York, Springer, 1999.

Y.C. Jiang and Y.M. Liu, The completeness of orthogonal wavelet systems in $ell^2(Z)$, Acta Mathematica Sinica, Chinese Series, 49(5): 1075-1085(2006).

Y.C. Jiang and Y. Liu, The compatibility of properties for discrete orthogonal wavelets,Journal of Beijing University of Technology (in Chinese), 32(4): 375-379(2006).

Y.C. Jiang, Realization of decomposition and reconstruction algorithms for discrete orthogonal wavelets, Application Research of Computers, 30(2): 420-423(2013).

A. Pevnyi and V. Zheludev, Construction of wavelet analysis in the space of discrete splines using Zak transform, Journal of Fourier Analysis and Applications, 8(1): 55-77 (2002).

A. Aldroubi and M. Unser, Oblique projections in discrete signal subspaces of $ell^2$ and the wavelet transform, Proc. SPIE, Wavelet Appl. in Signal and Image Processing II, 36-45 (1994).

A. Averbuch, A. Pevnyi and V. Zheludev, Biorthogonal Butterworth wavelet transforms derived from discrete interpolatory splines, IEEE Transactions on Signal Processing, 49(11): 2682-2692 (2001).




DOI: http://dx.doi.org/10.26713%2Fjims.v6i1.186

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