小波滤波器的统一构造方法与软件

尽管小波分析与应用已十分深入，特别是紧支集上的小波变换已广泛应用在信号处理，如何图象压缩、声音处理，文字识别等领域，但小波基或小波滤波器的构造却是一件十分取艰苦的工作，揭示了紧支集上任意长度正交小波基滤波器统一的解析结构。一种有限步递归构造分解方法可以非常容易地计算出任意 多个参数的正小波基滤波器参数。此后并验证了Ｄｕｂｅｃｈｉｅｓ等人的小波滤波器的构成参数，以及验证了已在具体应用中发挥重要作用的

General Construct Method & Software of Wavelet Base's Filter

Wavelet analyses have been used for many fields deeply, especially , the wavelet transforms on compact support sets have been applied to signal dealing and image compression etc. However, the constructing of wavelet base is a hard work to do. In this paper, for N=2k the analysis structure of wavelet base on compact support sets are found successful. That is the general solutions structure of equations which fits to the wavelet base orthogonal conditions, Those formulas or algorithms make it very easily construct many filters of wavelet base, at the same time , Daubechies's filters and some other filters which are important in apllications have been tested correct; With the aid of our formulas , it is very easy to dynamically choose the wavelet bases.