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Coefficient relation-based minimax design and low-complexity structure of variable fractional-delay digital filters

机译：基于系数关系的极小极大值设计和可变分数延迟数字滤波器的低复杂度结构

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摘要

Although the coefficient-relation of the even-order sub-filters in the Farrow structure has been revealed and adopted in the weighted-least-squares (WLS) design of even-order finite-impulse-response (FIR) variable fractional-delay (VFD) digital filters in the literature, it has never been exploited in implementing low-complexity VFD filters. This paper aims to (i) propose a low-complexity implementation structure through exploiting the coefficient-relation such that the coefficient-relation is not only utilized in the design process, but also utilized in the low-complexity implementation; (ii) formulate the minimax design of an even-order VFD filter through exploiting the coefficient-relation; (iii) propose a new two-stage scheme called increase-then-decrease scheme for optimizing the sub-filter orders so as to minimize the VFD digital filter complexity. With the above three advances, an even-order VFD filter can not only be designed and but also be implemented efficiently by exploiting the coefficient-relation. We will use a design example to illustrate the low complexity and high design accuracy.
机译：尽管Farrow结构中偶数子滤波器的系数关系已被揭示并在偶数有限脉冲响应（FIR）可变分数延迟的加权最小二乘（WLS）设计中采用（文献中的VFD）数字滤波器，在实现低复杂度的VFD滤波器方面从未得到开发。本文的目的是：（i）通过利用系数关系提出一种低复杂度的实现结构，使得系数关系不仅在设计过程中得到利用，而且在低复杂度实现中也得到利用； （ii）通过利用系数关系来制定偶数VFD滤波器的极小极大设计； （iii）提出了一种新的两阶段方案，称为先增后降方案，以优化子滤波器阶数，从而最大程度地降低VFD数字滤波器的复杂度。通过以上三个方面，不仅可以设计偶数VFD滤波器，而且还可以通过利用系数关系有效地实现该滤波器。我们将使用一个设计示例来说明低复杂度和高设计精度。

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