一种利用系统状态方程构造小波的方法

当使用小波解决问题时,得到的结果与所选用的小波有较大的关系.如何针对特定的问题来构造适用的小波还没有有效的方法.阐述了一种利用消失矩条件和线性时不变系统的状态方程来构造小波的方法.为此首先简要的介绍了Diophantine方程和消失矩条件,然后利用系统的模式函数可以从解状态方程的特征根得到的特性,通过添加令小波与模式函数正交的条件,得到了构造小波的方法.并进一步对用所推导的方法构造双正交关于0对称的实小波这一具体情况进行了讨论.最后给出了应用此方法构造小波的一个实际的例子.

Wavelet construction using state equation

The selection of wavelet plays an important role in the result when one uses wavelets to resolve problems. Unfortunately there is no effective way to construct proper wavelet for special problems. Motivated by the filter reconstruction and vanish-moment conditions, a general construction approach based on the state equation was proposed for linear time-invariant systems. First, the Diophantine equations and vanish-moment conditions were briefly introduced. Second, based on the exponential mode functions derived by the characteristic roots of the system, an orthonormal condition between mode and wavelet functions and algebraic equations were presented to construct the wavelet functions. Third, a bi-orthogonal real wavelet symmetry about 0 with odd length was constructed by using the proposed approach. Finally, an example was given to illustrate the construction approach.