基于高斯型窗函数的基小波构造

阐述了基于高斯型窗函数的可容基小波构造,讨论了若干类基小波.首先引入若干经典基小波如墨西哥草帽小波、莫莱小波、DOG犬小波和盖博解析小波,作者发现它们具有统一的结构,即均由高斯窗函数生成;进而在犬小波结构的启示下,构造了由高斯窗函数的差形成的犬小波族,对之验证了可容性条件;并且将它推广为有限个高斯窗函数的线性组合形成的小波,确定了带通条件.

On the Construction of Mother Wavelets Based on Gaussian-type Functions

We discuss some problems on the wavelet analysis.Firstly,we introduce some classical mother wavelets named after Mexican Hat,Morlet,DOG and Gabor.Then we derive that they have common structure,i.e,they are all of Gaussian-type.Inspired by the form of DOG wavelet,we construct a family of wavelets in the form of the difference of two Gaussian functions;Finally,we generalize the result to the case of the linear combination of finite Gaussian functions,defined as LOG wavelet in this paper.