多重对偶小波框架与波包框架的存在条件

Existence conditions of multiple dual wavelet frames and wave packet frames

针对对偶小波框架具有双正交基的某些性质,采用傅立叶分析方法与时频分析方法,研究了多重Gabor框架与多重对偶小波框架之间的联系.给出由一对多重对偶Gabor框架转换为多重对偶小波框架的新方法.运用双线性泛函和局部可积函数,得出了多重波包紧框架存在的条件.

Aimed at dual wavelet frames possessing some properties of bi-orthogonal wavelet bases,the relation of multiple Gabor frames to multiple dual wavelet frames is investigated by means of Fourier analysis and time-frequency analysis.A new method for conversion of a pair of multiple dual Gabor frames to multiple dual wavelet frames is presented.Existence conditions for multiple tight wave packet frames are obtained with bilinear functionals and locally integrable functions.