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

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.