中文摘要：

引入分数阶多分辨分析与分数阶尺度函数的概念．运用时频分析方法与分数阶小波变换，研究了分数阶正交小波的构造方法，得到分数阶正交小波存在的充要条件．给出分数阶尺度函数与小波的分解与重构算法，算法比经典的尺度函数与小波的分解与重构算法更具有一般性．

英文摘要：

The fractional multiresolution analysis and the fractional scaling functions are in- troduced. The constructive method for fractional orthogonal wavelets is researched by using time-frequency analysis methodand and fractional wavelet transforms. We derive a sufficient and necessary condition for fractional orthogonal wavelets. We develop a decom- position and reconstruction algorithm for the fractional scaling functions and fractional orthogonal wavelets which possesses more generality than the decomposition and recons- truction algorithm for the classical scaling functions and wavelets.