Minimum phase acoustic systems: An intuitive model study

Abstract

The zeros and poles of minimum phase systems lie within the unit circle in the z-plane, which ensures the existence of a stable inverse. In acoustics, the question if a system is minimum phase has important consequences, such as the ability to find an inverse of a room’s acoustic transfer function to compensate for reverberation. In this paper, we provide an intuitive model of minimum phase acoustic systems based upon physical arguments. Using the image method, we compute the transfer function of generic one, two, and three-dimensional acoustic enclosures with a sound source and a microphone placed at arbitrary locations. We find the relationship between the direct sound field and the reverberant sound field that ensures the minimum phase property of the system. Essentially, the system retains the minimum phase property if the radius of reverberation, i.e., the distance from the source where the direct sound and reverberant sound become equal in magnitude, lies outside of the boundaries of acoustic enclos...