On the phase condition and its solution for Hilbert transform pairs of wavelet bases
On the phase condition and its solution for Hilbert transform pairs of wavelet bases
复制标题
小波基希尔伯特变换对的相位条件及其求解
DOI：
10.1109/tsp.2003.818996
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Runyi Yu
中科院分区：
文献类型：
--
作者：
Hüseyin Özkaramanli;Runyi Yu
本文研究了两个小波基的尺度滤波器的相位条件，该相位条件使相应的小波成为Hilbert变换对。导出了一种替代的等效相位条件。与等效条件和使用傅立叶级数展开，我们表明，解决方案，相应的缩放滤波器是从另一个偏移了一半的样本是唯一的解决方案满足相位条件。
In this paper, the phase condition on the scaling filters of two wavelet bases that renders the corresponding wavelets as Hilbert transform pairs is studied. An alternative and equivalent phase condition is derived. With the equivalent condition and using Fourier series expansions, we show that the solution for which the corresponding scaling filters are offset from one another by a half sample is the only solution satisfying the phase condition.