【摘要】 本文基于小波理论框架,分析探讨了有关高斯函数的小波特性。根据多尺度微分算子理论和多分辨分析思想,证明了高斯函数构造了一个多分辨分析(MRA),高斯函数的各阶导数均构成小波基函数。从滤波器组的角度,由高斯函数的导数构成的小波函数构造了低通滤波器的脉冲响应,也可视为一尺度函数。更多还原

【Abstract】 This paper discusses the Gaussian function based the frame of wavelet theory. According to the theory of multi-scale differential operator, the derivation of Gaussian function can be seen as the prototype wavelet. The wavelet functions can construct the pulse response of the low-filtering groups from the filtering groups in the engineering. With the multi-resolution analysis,this paper proofs Gaussian function can construct MRA.更多还原