Explicit construction of symmetric orthogonal wavelet frames in L2(Rs)

Authors:
Youfa Li;Shouzhi Yang
Affiliations:
Department of Mathematics, Shantou University, Shantou 515063, PR China and College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, PR China;Department of Mathematics, Shantou University, Shantou 515063, PR China
Venue:
Journal of Approximation Theory
Year:
2010

Citing 2
Cited 1

Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix

Journal of Computational and Applied Mathematics - Special issue: Approximation theory, wavelets, and numerical analysis
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Bessel multiwavelet sequences and dual multiframelets in Sobolev spaces

Advances in Computational Mathematics

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Abstract

Recently, some researchers propose the concept of orthogonal wavelet frames, which are useful for multiple access communication systems. In this article, we first give two explicit algorithms for constructing paraunitary symmetric matrices (p.s.m. for short), whose entries are symmetric or antisymmetric Laurent polynomials. We also give two algorithms for constructing orthogonal wavelet frames from existing tight or dual wavelet frames in L^2(R^s). The constructed orthogonal wavelet frames are also tight or dual ones. Furthermore, based on the constructed p.s.m. and the existing symmetric tight (dual) wavelet frames, we can obtain symmetric orthogonal (s.o. for short) tight (dual) wavelet frames in L^2(R^s). From the constructed s.o. wavelet frames in L^2(R^s), we can obtain s.o. wavelet frames in L^2(R^m) by the projection method, where m@?s. To illustrate our results, we construct s.o. wavelet frames in L^2(R) and L^2(R^2) from the quadratic B-spline B"3(x). Especially, in Example 2, we obtain nonseparable tight 2I"2-wavelet frames in L^2(R^2) from a separable tight 2I"2-wavelet frame constructed by tensor product.