Variable Taylor realization and improved approximation of FIR fractional delay systems

Abstract

A modular realization, based on the Taylor structure, is proposed for a maximally flat fractional delay FIR systems. The realization enjoys independence of the multiplier coefficients to changes of the system order, availability of closed-form formulas and recurrence for the multiplier coefficients, requirement of one less multiplier coefficient compared to the direct-form realizations, and existence of schemes for efficient variable delay and order implementations. It is shown that for a variable delay structure, the coefficient updating operation can be performed efficiently using a simple recurrence, and the transient effects can be mitigated to at most two samples. A modified form of the structure with enhanced modularity is also proposed for odd-order systems. Two variable delay schemes are proposed for this modified structure: A transient-free scheme and a scheme that provides to gradually improve the approximations during the transient phase. A method is also proposed for improved approximation under a fixed total number of variable multiplier coefficients. © 1998 John Wiley & Sons, Ltd.