一类具有线性相位的二重多小波的构造

给出由实单一紧支撑正交的小波构造二重正交多小波的方法。具体地,首先由实单一的紧支撑尺度函数构造出单一紧支撑正交对称的复尺度函数,再由构造出的复尺度函数去构造二重正交紧支撑多尺度函数,然后给出由二重尺度函数构造二重小波的显式公式。紧支撑正交的单一小波除Haar小波外不具有任何对称性,它用作滤波器不可能有线性相位,而由实单一紧支撑正交的尺度函数构造出的二重尺度函数却是对称的,对应的二重小波可以是对称或反对称的,从而使得这种小波在信号处理的过程中具有线性相位。最后给出相应的构造算例。

Construction of Multiwavelets with Multiplicity 2 Possessing Linear Phase

The paper deseribes a method to derive orthogonal multiwavelets with multiplicity 2 from a class of uni-real-valued compactly supported orthogonal wavelet. Concretly, compactly supported orthogonal complex uni-scaling function is first constructed by real valued ones. Then multiscaling functions with multiplicity 2 with symmetry is constructed by the complex valued ones. Futhermore, the explict formula construted multiwavelets is obtained. As we know, with the exception of the Haar function, uni-real-valued orthogonal wavelet filter banks with compact support lack symmetry and do not possess linear phase. However, multiwavelets obtained by using our method have symmetry/antisymmetry and linear phase. Finally, design examples are given.