A new class of orthonormal symmetric wavelet bases using a complex allpass filter
A new class of orthonormal symmetric wavelet bases using a complex allpass filter
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使用复全通滤波器的一类新的正交对称小波基
DOI：
10.1109/78.960410
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
T. Yoshikawa
中科院分区：
文献类型：
--
作者：
Xi Zhang;Akira Kato;T. Yoshikawa
研究了由单个复全通滤波器组成的全样本对称准酉滤波器组的设计，给出了一类新的实值标准正交对称小波基。首先，从小波的对称性和正交性条件出发，推导出了复全通滤波器必须满足的条件，并给出了满足这些条件的传递函数。其次，从正则性和频率选择性的角度出发，利用导出的传递函数设计了准酉滤波器组；提出了一种设计给定平面度的准酉滤波器组的新方法。该方法是基于利用Remez交换算法对广义特征值问题的表述。因此，通过求解特征值问题可以很容易地得到滤波系数，并且通过几次迭代即可得到最优解。此外，所提出的方法还包括极大平解和极小极大解作为两种具体情况。最平坦的过滤器具有不需要任何迭代的封闭形式的解。最后，通过设计实例验证了所提方法的有效性。
This paper considers the design of the whole sample symmetric (WSS) paraunitary filterbanks composed of a single complex allpass filter and gives a new class of real-valued orthonormal symmetric wavelet bases. First, the conditions that the complex allpass filter has to satisfy are derived from the symmetry and orthonormality conditions of wavelets, and its transfer function is given to satisfy these conditions. Second, the paraunitary filter banks are designed by using the derived transfer function from the viewpoints of the regularity and frequency selectivity. A new method for designing the proposed paraunitary filterbanks with a given degrees of flatness is presented. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez exchange algorithm. Therefore, the filter coefficients can be easily obtained by solving the eigenvalue problem, and the optimal solution is attained through a few iterations. Furthermore, both the maximally flat and minimax solutions are also included in the proposed method as two specific cases. The maximally flat filters have a closed-form solution without any iteration. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method.