【摘要】 通过将分数阶Fourier变换(Fr FT)与传统小波框架(WF)相结合,本文引入了一类新的框架,即广义小波框架(GWF).首先介绍了分数阶Fourier变换、级数以及相关结论;然后通过分析母小波的Fourier变换,得到了L2(R)中广义小波框架的若干个充分条件和必要条件;最后在参数选择为a=2,b=1的特殊情形下,给出了L2(R)中紧广义小波框架的一个充要条件.更多还原

【Abstract】 The main purpose of this paper is to discuss generalized wavelet frames(GWF), which is based on fractional Fourier transform and wavelet frames. By analyzing Fourier transformation of the mother wavelets, we show several sufficient conditions and necessary conditions for GWF of L2(R). At last, when the parameters are selected by a = 2 and b = 1 as a special condition, a necessary and sufficient condition is given for tight GWF.更多还原