In room acoustic simulations, surface materials are commonly represented by energy parameters such as absorption and scattering coefficients, which do not carry phase information. This paper presents a method for transforming statistical absorption coefficients into complex surface impedances, which are required for phased or time-domain calculation methods. An impedance model based on fractional calculus is proposed to provide a general model for common acoustic materials. The parameters governing the model are determined by solving an optimization problem, with constraints ensuring that the resulting impedance has a physical meaning and respects causality in the time domain.

Known material models, such as Miki’s and Maa’s models, are used as references to assess the validity of the proposed approach. Due to the non-uniqueness of retrieving complex-valued impedances from real-valued absorption coefficients, prior information about the absorber of interest can be incorporated as constraints, which is shown to help determine the correct impedance from the absorption coefficient. Further stability and sensitivity investigations indicate that the presented method constitutes an efficient solution for converting sound absorption coefficients back into their original complex surface impedances.