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

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. ► We propose a low-complexity structure for implementing even-order VFD filters. ► An SOCP minimax design is proposed by utilizing the coefficient-relation. ► We propose a two-stage scheme for optimizing the even-order sub-filter orders. ► An example is given for illustrating both the implementation and design.