The Traits of Orthogonal Nonseparable Binary-Variable Wavelet Packs in Two-Dimensional Function Space - Advanced Research on Computer Education, Simulation and Modeling - page 59

The Traits of Orthogonal Nonseparable Binary-Variable
Wavelet Packs in Two-Dimensional Function Space

Guoqiang Wang * and Rui Wei

Department of Computer Science, Huanghuai University, Zhumadian, 463000, China
[e-mail]

Abstract. In this paper, the concept of orthogonal non-tensor bivariate wavelet
packs, which is the generalization of orthogonal univariate wavelet packs, is pro
-posed by virtue of analogy method and iteration method. Their orthogonality
property is investigated by using time-frequency analysis method and variable
se-paration approach. Three orthogonality formulas concerning these wavelet
packs are obtained. Moreover, it is shown how to draw new orthonormal bases
of space

LR from these wavelet wraps. A procedure for designing a class of
orthogonal vector-valued finitely supported wavelet functions is proposed by
virtue of filter bank theory and matrix theory.

2 ()

Keywords: Nonseparable; binary wavelet packs; Sobelev space; Bessel sequen-
ce; orthonormal bases; time-frequency analysis method.

1 Introduction and Notations

Although the Fourier transform has been a major tool in analysis for over a century, it
has a serious laking for signal analysis in that it hides in its phases information con-
cerning the moment of emission and duration of a signal. Wavelet analysis [1] has
been developed a new branch for over twenty years. Its applications involve in many
areas in natural science and engineering technology. The main advantage of wavelets
is their time-frequency localization property. Many signals in areas like music,
speech, images, and video images can be efficiently represented by wavelets that are
translations and dilations of a single function called mother wavelet with bandpass
property. Wavelet packets, owing to their good properties, have attracted considerable
attention. They can be widely applied in science and engineering [2,3]. Coifman R. R.
and Meyer Y. firstly introduced the notion for orthogonal wavelet packets which were
used to decompose wavelet components. Chui C K.and Li Chun L.[4] generalized the
concept of orthogonal wavelet packets to the case of non-orthogonal wavelet packets
so that wavelet packets can be employed in the case of the spline wavelets and so on.
Tensor product multivariate wavelet packs has been constructed by Coifman and
Meyer. The introduction for the notion on nontensor product wavelet packs attributes
* Corresponding author.