At the same time , it is desirable for wavelet possess orthogonality , symmetry , short support and higher vanishing moments simultaneously , this leads to the advent of the multiwavelets 同时人们也希望所用的小波基会同时拥有正交性，对称性，紧支性和高阶消失矩，这又导致了多小波理论的诞生。
The results obtained in this dissertation include the following four aspects : ( 1 ) according to the theory of 2d lagrangian interpolation , interpolating wavelets be researched 在小波理论的研究及应用方面，小波基的构造是一个重要的研究方向。在一维情形，无论是理论还是应用都得到深入的研究。
Based on this idea , in this paper , we used an infinitely differentiable wavelet with a local support . its properties are different from those of orthonormal wavelet bases 基于这一思想，本课题所使用的小波不象一般的正交小波基局部性和正则性是冲突的，相反，它既是局部支撑的，又是无限光滑的。
Based on invariability of the quality factor of wavelet transform , combined with proper wavelet group , this paper discusses the application of wavelet transform in the detection of backscatter signal 摘要基于小波变换品质因数不变性的特点，结合适当的小波基，探讨小波变换在回波信号检测中的算法。
Thirdly , the theories of wavelet transform in image compression were described . with the analysis on distribution of the transform coefficient , it is proven that zero - tree structure is the best choice 改进算法包括了以下几个方面：对图像进行小波变换时，选择了更合适图像编码的z97双正交小波基。
But now the field is finite that wavelet analyses is used in the ultrasonic testing signal processing , and the problem of selecting the best wavelet did n ' t be considered in the application of wavelet 但目前小波分析处理超声检测信号的应用领域还很有限，并且应用过程中没有考虑最优小波基的选取问题。
Finally , a factual image compression method based on wavelet transform is offered . the main work is listed as follows : 1 ) in this part , the orthogonal daubechies wavelet bases from 1 to 4 are analyzed 本文所作主要工作具体如下： 1 )按照小波基的选取原则，通过对性能优良的daubechies的1到4阶正交小波基的验证，得到了实际的仿真结果数据。
The method about constructure of a new compactly supported orthonormal wavelet and scale function concerned is put forward and the exponent regularity of the kind of wavelet and related scale function is estimated accurately 提出了一类新的具有紧支集的标准正交小波基以及相关的尺度函数的构造方法，准确估计了该类小波和相关尺度的正则性指数。
To choose wavelet function based on time - frequency region is put forward , time - frequency region composing of all of these wavelet functions can overlay wholly time - frequency region of non - linear function to approximate 本文提出了根据逼近函数的时频空间区域来选择小波基函数，使这些小波基函数共同构成的时频空间区域覆盖完逼近函数的时频空间区域。
