State Space and Transfer Function Modeling of Evanescent Waves in Two-Dimensional Acoustics

With intense current interest in active noise control, it is desirable to develop models of acoustic phenomena that are useful for state-space-based control methodologies. Consequently, this paper extends the one-dimensional modeling of acoustic transfer functions developed in earlier work to the case of two-dimensional acoustics. This extension must therefore account for the phenomenon of evanescent waves, which are non-propagating and thus affect only the near field. While evanescent waves are well understood within the context of wave models, their presence is less apparent in state space-based model modals. This paper thus presents a derivation of state space models for two-dimensional acoustics which are shown to predict the presence of evanescent waves.