【摘要】 针对分数阶Fourier变换在信号处理中应用的广泛性,引入了分数阶尺度函数与分数阶小波变换的概念.运用分数阶Fourier变换与时频分析方法研究了分数阶多分辨分析与尺度函数的构造方法,刻画分数阶尺度函数的特征.得到分数阶尺度函数存在的充要条件.更多还原

【Abstract】 Aiming at the application of fractional Fourier transform which is widely used in the signal processing,we draw into the fractional scaling functions and the fractional wavelet transform.We research into constructive methods for the fractional multiresolu-tion analysis and the fractional scaling functions by virtue of fractional Fourier transform and timefrequency analysis.The characterization for the fractional scaling functions is described.A sufficient and necessary condition for the existence of the fractional scaling functions is proposed.更多还原