Evaluation of decay times in coupled spaces: An efficient search algorithm within the Bayesian framework

Abstract

This paper discusses an efficient method for evaluating multiple decay times within the Bayesian framework. Previous works [N. Xiang and P. M. Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001); 113, 2685-2697 (2003); N. Xiang, P. M. Goggans, T. Jasa, and M. Kleiner, 117, 3707-3715 (2005)] have applied the Bayesian inference to cope with demanding tasks in estimating multiple decay times from Schroeder decay functions measured or calculated in acoustically coupled spaces. Since then a number of recent works call for efficient estimation methods within the Bayesian framework. An efficient analysis is of practical significance for better understanding and modeling the sound energy decay process in acoustically coupled spaces or even in single spaces for reverberation time estimation. This paper will first formulate the Bayesian posterior probability distribution function (PPDF) in a matrix form to reduce the dimensionality as applied to the decay time evaluation. Based on existence of only global extremes of PPDFs as observed from extensive experimental data, this paper describes a dedicated search algorithm for an efficient estimation of decay times.