基于非正交实小波的框架扩展方法及滤波应用

Non orthogonal Real Wavelet Based Frame spanning and Its Application in Filtering

该文由框架定义导出其自扩展性，并在此理论基础上把调制思想运用于小波变换，提出了一种基于非正交实小波的框架扩展方法，并以墨西哥草帽小波为例对该方法给予详细的说明。使用该方法可以构造出具有正交小波尺度函数特性的框架———调制小波，这种调制小波不但具有优良的滤波特性，而且对噪声具有鲁棒性，还兼有窗函数易于实现的优点。

Self spanning property of the Frame is deduced from its definition.Based on this theory,the modulating method is introduced in wavelet transform and therefore a method on how to span a frame from Non orthogonal Real Wavelet is presented.Its spanning method is illustrated in details by Mexico Hat Wavelet.The frames spanned by this method (named modulated wavelet) share many properties of scaling function of orthogonal wavelets and possess excellent filtering property,robustness to noises and easily realizing property of window functions.