Design of Even-Order Variable Fractional Delay FIR Filters based on Pivot Element Weighting Iterative Algorithm

Abstract

This paper proposes a design for even-order variable fractional delay (VFD) finite impulse response (FIR) filters based on pivot element weighting iterative (PEWI) algorithm. Initially, a mathematical model is established for even-order VFD FIR filters to derive the actual variable frequency response (VFR). This VFR is then employed to calculate the error between the actual and ideal VFRs, which is decomposed into real and imaginary components. The design aims to minimize these errors, inherently involving the solution of ill-conditioned system of linear equations. The PEWI algorithm is designed to address these equations, thereby minimizing the real and imaginary VFR errors to determine the optimal coefficients for even-order VFD FIR filters. Comparative examples with linear programming (LP) and second-order cone programming (SOCP) methods demonstrate the enhanced effectiveness and the reduced computational complexity of our PEWI-based design over LP and SOCP.