Uncertainty principle for energy decay analysis: Efficiency and accuracy of Bayesian methods

OpenAlex İngilizce

The analysis of sound energy decay is of fundamental importance for a broad range of room-acoustic applications. This paper addresses the efficiency of analyzing energy decays concerning analysis uncertainties within a Bayesian framework. Previous efforts by Xiang, Goggans, Jasa, and Robinson [J. Acoust. Soc. Am. 129, 741-752 (2011)] have established a parametric model derived from Schroeder integration that decomposes the Schroeder decay functions into single or multiple exponential decays. This model facilitates advanced methods for energy decay analysis in rooms. A wide range of data resolutions can meet the need of room-acoustic decay analysis. However, for high efficiency, acousticians can involve lower resolutions, still adequately representing energy decay processes. This paper discusses conditions for representing Schroeder integration by desirable, sufficiently less data points for higher efficiency of the decay parameter estimation. The condition is put within the context of the uncertainty principle originating from quantum mechanics. At the same time, increased efficiency is associated with uncertainties. Within the Bayesian framework, the numerical uncertainties are investigated against those of the experimental measurements. Using experimental data in performing arts venues, this work quantifies uncertainties to leverage adequate accuracy and efficiency of the analysis.