Schroeder integration: Foundation for advanced sound energy decay analysis.

Abstract

Schroeder’s backward integration method broke the new ground in classical architectural acoustics. Soon after publication of Schroeder’s backward integration method for obtaining sound energy decay functions from room-impulse responses [Schroeder, J. Acoust. Soc. Am. 37, 409–412 (1965)], research activities in this field have been frequently reported in major journal publications. For reverberation time estimation based on a traditional straight-line model, solutions to remedy problems related to the upper limit of backward integration and the background noise in experimentally measured Schroeder decay functions have emerged. Using a parametric model derived from the nature of Schroeder integration, this author proposed a nonlinear regression method [Xiang, J. Acoust. Soc. Am. 98, 2112–2121 (1995)]. The nonlinear regression method yields reverberation time estimates, insensitive to background noise, and the upper limit of integration. Recent interest in acoustically coupled-volume systems has prompted new challenges in analyzing sound energy decay characteristics, which are more complicated than just single-rate decays. This paper will demonstrate a suitable framework for this room-acoustics application using Bayesian inference and the Schroeder backward integration as the foundation of the advanced model-based energy decay analysis. Based on the Schroeder integration, two levels of inference, decay order selection, and decay parameter estimation have been developed for practical applications.