Reverberant phase in a room and zeros in the complex frequency plane

Abstract

Transfer function (TF) phase of finite-damped systems can be estimated from the distribution of poles and zeros in the complex frequency domain. This paper investigates the distribution of nonminimum phase zeros of TFs from impulse response data measured in a reverberant space for which the modal overlap is large. The number of nonminimum phase zeros is found to be inversely proportional to the damping of the system. This result is shown to be consistent with earlier work on the relation between phase and energy decay. The distribution of zeros and the phase of transfer function are also changed by windowing the impulse response. An exponential window is recommended in order to reduce the effect of truncation on the zeros, although such a window will have the effect of added damping.