基于高斯函数的小波系及其快速算法

The Wavelet Series Based on Gaussian Function and Its Fast Algorithm

系统地探讨了由高斯函数各阶导数所构成的小波系及其性质 ,计算表明其第n阶导数具有n阶消失矩 .文中以高斯函数为尺度函数 ,讨论了高通滤波器和低通滤波器的特殊关系 ,并给出了以高斯函数 1到 6阶导数作为小波时快速算法所需要的滤波器系数 .

The wavelet series made up of different derivatives of Gaussian function and their specialities are discussed systematically in this paper. The computed results show that the n _th derivative of Gaussian function has vanishing moment of n _th order. Gaussian function being scaling function, the special relationship between high pass filter and low pass filter is discussed. The filter coefficient for fast algorithm is also given.