Design of linear-phase IIR integrators with maximally-flat and Chebyshev magnitude responses

Abstract

This paper proposes two methods for designing linear-phase infinite impulse response integrators. The first method, referred to as the maximally-flat one, imposes flatness conditions on the frequency response error function, leading to a system of linear equations that have to be solved to determine unknown coefficients. Furthermore, a relation is established between the proposed maximally-flat integrators and existing integer-order linear-phase integrators derived using the algebraic polynomial-based quadrature rules, demonstrating that the latter represent special cases of the proposed integrators. The second method, referred to as the optimal one, minimizes the complex frequency response error function in the weighted Chebyshev sense, which is achieved by an efficient exchange algorithm that exhibits rapid convergence. The proposed linear-phase integrators are also compared with several existing linear- and nearly linear-phase integrators.