Impedance and Its Time-Domain Extensions

The classical concept of impedance as a means to characterize the ree ectivity and absorption of a surface to the incident waves has always been a complex-valued quantity akin to plane harmonic waves and the analysis of their ree ections. A new look at this classical quantity irrespective of the type of incident waves is presented. It points out that a direct operational inversion of impedance into time-domain boundary operators will, in general, lead to an unstable system, whereas the inversion of the corresponding ree ection coefe cient will result in stable, easily implementable boundary operators for time-domain prediction of wave ree ection. It reveals the equivalent, pulselike, causal process of time convoluting the incident wave into the ree ected wave. Excellent agreement with analytical solutions derived here and from other sources supports the validity of the approach and demonstrates the accuracy of the implementations.