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To design a variable recursive digital filter whose stability is always guaranteed, it is necessary to ensure that the stability conditions are always satisfied in the tuning process. Furthermore, it is also necessary to keep a certain margin for the stability (stability margin) in such a way that some unpredictable environmental changes and coefficient-value deviations will not cause instability. To add a stability margin to the stability of the second-order (2nd-order) recursive filter, this paper first introduces a stability trapezoid by trimming the well-known stability triangle of the 2nd-order recursive digital filter. Then, we quantitatively analyze the upper bound for the stability margin by using a stability-margin parameter. This theoretical stability-margin analysis is fundamental to the design of a variable recursive filter with an expected stability margin. Finally, we utilize a demonstrative example to verify the consistence between the theoretical upper bound of the stability margin and the computer simulation results. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]