Coefficient-Symmetries for Implementing Arbitrary-Order Lagrange-Type Variable Fractional-Delay Digital Filters
Coefficient-Symmetries for Implementing Arbitrary-Order Lagrange-Type Variable Fractional-Delay Digital Filters
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DOI：
10.1109/tsp.2007.893967
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发表时间：
2007-08
影响因子：
5.4
通讯作者：
T. Deng
中科院分区：
文献类型：
--
作者：
T. Deng
在本文中，我们首先推导出一个显式公式，将任意阶拉格朗日型可变分数延迟（VFD）数字滤波器的系数表示为 VFD 参数 的多项式，然后为偶数阶和奇数阶拉格朗日型 VFD 滤波器系数开发一些有用的对称性。系数对称性有助于评估 VFD 滤波器系数以及可变频率响应，同时降低计算复杂性。更重要的是，可以利用系数对称性来有效地实现偶数阶和奇数阶拉格朗日型 VFD 滤波器，如 Farrow 结构和一种更高效的偶奇结构，使得子滤波器具有对称或反对称系数，从而节省了 VFD 滤波器系数的存储空间，并将 VFD 滤波过程中所需的乘法次数减少了近乎 50%。因此，利用系数对称性不仅可以加速 VFD 滤波，还可以降低实施成本。
In this paper, we first derive an explicit formula for expressing the coefficients of an arbitrary-order Lagrange-type variable fractional-delay (VFD) digital filter as polynomials of the VFD parameter , and then develop some useful symmetries for both even- and odd-order Lagrange-type VFD filter coefficients. The coefficient-symmetries facilitate the evaluations of VFD filter coefficients as well as variable frequency responses with reduced computational complexity. More importantly, the coefficient-symmetries can be exploited for efficiently implementing both even- and odd-order Lagrange-type VFD filters as Farrow structure and a more efficient one called even-odd structure such that the subfilters have symmetric or anti-symmetric coefficients, which saves the storage for VFD filter coefficients and reduces the number of multiplications required in VFD filtering process by almost 50%. Therefore, exploiting the coefficient-symmetries not only speeds up the VFD filtering, but also reduces implementation cost.