Digital IIR Integrator Design Using Richardson Extrapolation and Fractional Delay

In this paper, a new design of digital integrator is investigated. First, the trapezoidal integration rule and differential equation are applied to derive the transfer function of the digital integrator. The Richardson extrapolation is then used to generate high-accuracy results while using low-order formulas. Next, the conventional Lagrange finite-impulse response fractional delay filter is directly applied to implement the designed integrator. Two implementation structures are studied: direct substitution and polyphase decomposition. Finally, numerical comparisons with conventional digital integrators are made to demonstrate the effectiveness of this new design approach.