Design of orthonormal symmetric wavelet filters using real allpass filters
Design of orthonormal symmetric wavelet filters using real allpass filters
复制标题
使用实数全通滤波器设计正交对称小波滤波器
DOI：
10.1016/s0165-1684(00)00055-4
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
T. Yoshikawa
中科院分区：
文献类型：
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作者：
Xi Zhang;Tomonobu Muguruma;T. Yoshikawa
本文利用全通滤波器构造了一类实值正交对称小波滤波器，并提出了一种设计具有给定平坦度的全通小波滤波器的新方法。所提出的方法是基于制定的广义特征值问题，通过使用Remez交换算法，并考虑平坦性条件。因此，一组滤波器系数可以很容易地通过求解特征值问题来计算，并且通过几次迭代就可以获得极大极小意义下的最优解。此外，基于最大平坦全通的小波滤波器的设计也被包括作为特定情况，但它具有与Selesnick（IEEE Trans. Signal Process. 46（4）（1998年4月）1138-1141），从而不需要迭代过程。最后，设计了一些例子来研究滤波器的特性，并表明延迟元件的数量强烈影响滤波器的幅度响应。
In this paper, a class of real-valued orthonormal symmetric wavelet filters is constructed by using allpass filters, and a new method for designing the allpass-based wavelet filters with the given degrees of flatness is proposed. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez exchange algorithm and considering the flatness condition. Therefore, a set of filter coefficients can be easily computed by solving the eigenvalue problem, and the optimal solution in the minimax sense is obtained through a few iterations. Furthermore, the design of the maximally flat allpass-based wavelet filters is also included as a specific case, but it has a closed-form solution that is the same as in Selesnick (IEEE Trans. Signal Process. 46 (4) (April 1998) 1138–1141) so that the iteration procedure is not needed. Finally, some examples are designed to investigate the filter characteristics, and it is shown that the number of delay elements strongly influences the filter magnitude responses.