基于准确重建滤波器组的小波构造

Wavelet Construction Based on Perfect Reconstruction Filter Banks

小波应用领域广泛,因此对具有良好特性的新小波需求很大。传统的小波构造方法复杂,不利于构造各类适合不同问题求解的小波。分析了准确重建滤波器组的双正交性,基于准确重建滤波器组构造了一类新小波,并在紧支撑区间上得到尺度函数、小波函数、对偶尺度函数和对偶小波函数的图形。

The new wavelets of satisfactory characteristics were in great needs, for wavelets can be applied in vast fields. Traditional wavelets construction methods were complex and consequently are not favorable for creating various types of wavelets, which can be used to solve different problems. The biorthogonal property of the perfect reconstruction filter banks was analysed and build a new class of wavelets based on the perfect reconstruction filter banks. The scaling function, wavelet funcion, dual scaling function and dual wavelet function were obtained on the compact support.