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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.
Based on the Gaussian window function, this paper introduces some basic wavelet constructions based on Gaussian window function, and discusses some fundamental wavelets.Firstly, we introduce several classical wavelet bases, such as Mexican straw hat wave, Morlet wavelet, DOG dog wavelet and Gabor analytic wavelet, , Which are all generated by Gaussian window function. In the light of the dog wavelet structure, the dog wavelet family formed by the difference of Gaussian window function is constructed, which verifies the acceptability condition and extends it to a finite number A linear combination of Gaussian window functions forms a wavelet that determines the bandpass condition.