构造正交小波基的基本方法之一

A Basic Method to Build an Orthogonal Wavelet Basis

本文不仅给出一种构造局部性好的正交小波基的方法,并且给出了构造各种优良性质的正交小波基的一般思想方法。其特点:使构造的小波母函数有具体的表达式,既有较好的光滑性,又有很好的局部性,并且其收敛速度与│t│^（-（3k+1））同阶,其中k为任意自然数。这种方法不需要每次重新构造函数,只要改变k的值,就能满足不同实际问题的需要。

This paper presents not only a luothod to build an orthogonal wavelet basis of locality wcli but also a general mothod to build an orthogonal wavelet basis of all kinds of good quality. Its character: mother wavelet has concrete expression, better properties in smoothners and locality. This wavelet's order at which it converges to zero can reach to O(|t|-(3k+l), the k is arbitrary natural number. This method needn't rebuild function only if k is changed. This method can satisfiet all kinds of goals.