English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, the concepts and related conclusions of two-direction multiresolution analysis and two-direction refinable functions are introduced; two-direction wavelet with scale 2 is researched and is extended to orthonormal symmetric and antisymmetric two-direction wavelet with scale M and relevant properties are obtained. A condition that 2 L stable solution of two-direction refinable functions can create for MRA is given; finally construction of two-direction wavelet by two-direction compactly orthonormal refinable functions is discussed. Introduction Wavelet analysis theory originated in the 1970 s, it is a rapid development of new fields. At present, it has been widely used in signal analysis, image processing, Quantum mechanics, theoretical physics; Military electronic countermeasures and weapons intelligent; Computer classification and recognition; Music and language of synthetic; Medical imaging and diagnosis; Seismic data processing; Large mechanical fault diagnosis, etc [1-4]. The different wavelet has been constructed according to the actual needs. Daubechies [5] have proved that in addition to haar wavelet beyond, for with orthogonal, symmetry and compact support with 2-band wavelet was not exist. In order to solve this problem, People have taken 2-band wavelet spread to multiwavelet, multidimensional wavelets and made a deep research and gave the structure method. However, due to the Multiwavelets its limitations, there may be problems in the practical application. Literature [10-11] have detailed explore the multiwavelets balance problems. Yang S Z [12-13] put forward the concept of two-direction refinable functions, and introduces the bidirectional orthogonal scaling function and wavelet function, and then got a few more practical theory and application results. Two-direction refinement equation is the promotion of refinement equation, So based on the bidirectional orthogonal refinement function can get good nature of the two-direction orthogonal wavelet. Xie C Z [14-15] researched the nature of the two-direction wavelet, and gives the structure two-direction wavelet method and example. This text combining with the two-direction wavelet, symmetric antisymmetric and promote literature 2-scale orthogonal symmetric wavelet to M-scale orthogonal symmetric and antisymmetric. Symmetric and antisymmetric two direction wavelet as a kind of new wavelet, it can be more widely used in more fields in real life. Orthonormal Two-Direction Refinable Function and Two-Direction Multi-Resolution Analysis Suppose ) ( 2 R L ∈ φ is two-direction refinable functions, satisfies ) ( ) ( ) ( mx k p k mx p x k Z k k − + − = −

proceedings of the 2nd international conference on systems engineering and modeling

Construction of compactly supported orthonormal symmetric and antisymmetric two-direction refinable functions and its corresponding wavelet with scale M