摘要
本文研究了调制高斯函数的小波变换.利用再生核函数的特殊技巧,得到了该小波变换的等距恒等式和像空间的结构,同时给出了该小波变换的采样定理,使得小波变换能用再生核函数表示.这为一般的小波变换的像空间的研究提供了理论基础.
In this paper, the wavelet transform of a modulation Gaussian function is introduced. In virtue of the special technique of reproducing kernel function, the isometric identity and the structure of the image space of the wavelet transform are obtained. Meanwhile the sampling theorem of the wavelet transform is given. Consequently, wavelet transform can be represented by reproducing kernel function. This provides the theoretical foundation for further exploitation about the image space of general wavelet transform.
出处
《数学杂志》
CSCD
北大核心
2008年第5期507-513,共7页
Journal of Mathematics
基金
National Natural Science Foundation of China ( No.10571037)
Heilongjiang Education Foundation(No .1054G010)
关键词
小波变换
再生核
采样定理
wavelet transform
reproducing kernel
sampling theorem
