Retrieving complex surface impedances from statistical absorption coefficients

In room acoustic simulations the surface materials are commonly represented with energy parameters, such as the absorption and scattering coefficients, which do not carry phase information. This paper presents a method to transform statistical absorption coefficients into complex surface impedances which are needed for phased or time-domain calculation methods. An impedance model based on fractional calculus is suggested to achieve a general model for common acoustic materials. The parameters governing the model are determined by solving an optimisation problem, with constraints ensuring that the impedance found has a physical meaning and respects causality in the time domain. Known material models, such as Miki’s and Maa’s models, are taken as references to assess the validity of the suggested model. Due to the non-uniqueness of retrieving complex-valued impedances from real-valued absorption coefficients, prior information about the absorber of interest can be used as constraints, which is shown to help determine the
correct impedance from absorption coefficient. Further stability and sensitivity investigations indicate that the method presented constitutes an efficient solution to convert sound absorption coefficients back to their original complex surface impedances.