A new approach for the design of fractional delay by an FIR filter

Abstract

Fractional delay filters modeling non-integer delays are digital filters which ideally have flat group delays. In this letter, a new, simple, accurate and efficient FIR filter design to implement the digital ideal fractional delay is presented. The design technique is based on the MacLaurin series expansion formula which is applied to a given function to obtain a closed form FIR digital filter approximation of the digital ideal fractional delay operator z^-α. The obtained FIR filter approximation formula of the digital ideal fractional delay operator z^-α is similar to the well known Grünwald-Letnikov FIR digital filter approximation formula of the ideal analog fractional differentiator s^α. Some examples have been presented to illustrate the performance and the effectiveness of this new design method. Some comparisons results show that the proposed design yields better performances than the existing designs in the literature.

Keywords: Fractional delay FIR filter; Fractional delay operator; MacLaurin series expansion formula.