Physically Admissible Impedance Models for Time-Domain Computations of Outdoor Sound Propagation

Conditions for an impedance model to be physically admissible are checked for some popular models in the outdoor sound propagation community. They require that the definition of the impedance model is extended in the whole complex plane and that its inverse Fourier transform is real, causal and passive. For the many impedance models that are written as the square-root of a rational function, such as the Zwikker and Kosten model, the four-parameter Attenborough model and the Hamet and Bérengier model, these conditions are shown to be satisfied for a semi-infinite ground and for a rigidly backed layer. The case of polynomial type models is then investigated. The Delany and Bazley model is not physically admissible as it is real or causal depending on its extension in the complex plane, but it can not simultaneously fulfill both conditions. The Miki model for a rigidly backed layer does not satisfy also the passivity condition as its real part is negative for low frequencies. A new polynomial model is thus proposed and is shown to be physically admissible. PACS no. 43.28.En 1