On the Construction of Mother Wavelets Based on Gaussian-type Functions
Zheng Xun-ye · Shuxue de shijian yu renshi · 2008
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.