逼近希尔伯特变换对的小波基的设计

很多研究者已经证实在信号处理中利用一对小波变换能够获得显著的改进，其中这一对小波形成一对希尔伯特变换对。基于谱分解本文构造了互为希尔伯特变换对的二进小波基对。但是从一个已知的小波出发，利用它的希尔伯特变换来得到第二个小波，此时第二个小波不会是有限支撑的。本文设计一个有限支撑的小波去逼近无限支撑的小波。这个方法和Daubechies构造带有消失距的紧支撑小波的方法很相似，只是逼近希尔伯特变换要用到一个平坦延迟的滤波器。

The Design of Approximate Hilbert Transform Pairs of Wavelet Bases Based on Remote Sensing and GIS

Many researchors have demonstrated that significant improvements can be obtained in wavelet signal processing by utilizing a pair of wavelet transforms where the wavelets form a Hilbert transform pair. This paper describes design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases. But one could start with a known wavelet and take its Hilbert transform to obtain the second wavelet, in that case the second wavelet would not be of finite support . This paper design a finitely supported wavelet to approximate the infinitely supported wavelet . This approach is analogous to the Daubechies construction of compactly supported wavelets with vanishing moments but where the approximate Hilbert transform will use a flat delay filter.