Interpolation-based optimal s-to-z mapping functions for IIR design

Abstract In this paper, novel low-order s-to-z mapping functions are proposed. The methodology employs an interpolation framework that combines the first-order bilinear transform and the Adams-Moulton numerical integration formula, utilizing distinct interpolating variables. The resulting transfer functions effectively map the s-plane to the z-plane, achieving an accurate approximation of the ideal magnitude and phase response in the transition from the analog to the digital domain. Notably, the relationship between the analog frequency (Ω) and the discrete frequency (ω) exhibits maximal linearity over an extended frequency range, rendering the proposed approach highly suitable for infinite impulse response (IIR) filter design. Furthermore, the derived mapping functions are applied in the design of digital low-pass filters for various quality factor values. Simulation results demonstrate a significant enhancement in the frequency response within the digital domain compared to existing mapping techniques. Additionally, experimental validation is conducted using a Simulink-based design model, confirming the efficacy of the proposed approach.