This paper presents a multisegment optimization design algorithm for both even- and odd-order variable fractional-delay filters. The proposed algorithm is based on segmenting the fractional delay and separately solving the filter coefficients in each segment. Moreover, the lower bound of the polynomial order and the upper bound of the subfilter design error are derived. These bounds enable us to prove that the proposed algorithm effectively reduces the implementation complexity at the expense of storage resources. Hence, a joint search algorithm is proposed to find the lowest polynomial orders and subfilter orders that meet the filter specifications. Simulations and comparisons are conducted to illustrate the superiority of the proposed algorithm in terms of the implementation complexity over existing methods under common specifications.

本文提出了一种针对偶数和奇数阶可变分数延迟滤波器的多段优化设计算法。所提出的算法是基于分段分数延迟并分别求解每个分段中的滤波器系数。此外，得出多项式阶数的下限和子滤波器设计误差的上限。这些界限使我们能够证明所提出的算法以存储资源为代价有效地降低了实现复杂度。因此，提出了一种联合搜索算法，以找到满足滤波器规格的最低多项式阶数和子滤波器阶数。进行仿真和比较，以说明所提出算法的实现复杂性优于通用规范下现有方法的优越性。