The invertibility of acoustic systems has significant consequences for a number of applications such as room equalization and reverberation cancellation. Invertibility of a system is assured when it is minimum phase, i.e., if the system has no zeros or poles outside of the unit circle in the z-plane. For a nonminimum phase system, with zeros or poles exterior to the unit circle, the inverse is either unstable or non-causal. This discussion, couched in mathematical terms, gives little insight into the physical origin of minimum versus nonminimum phase system behavior. The purpose of this paper is twofold. First, the paper aims to provide an overview of the concepts and methods for assessing the invertibility of the response of acoustic systems. Second, the paper provides a physically intuitive picture of minimum versus nonminimum phase response in acoustic systems. We consider an acoustic system composed of a loudspeaker and a receiver placed at arbitrary locations within a reverberant rectangular enclosure. We then find the relationship that must exist between the direct and the reverberant sound fields to ensure that the system remains minimum phase. We then describe a simple scheme for finding the frequencies at which nonminimum phase behavior appears.

This content is only available via PDF.