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 nonpropagating 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