Room acoustic modal analysis via model-based Bayesian inference

Abstract

This work illustrates the application of Bayesian Inference in analyzing modal behavior in an experimentally measured room impulse response at a single location. The Prony Model is employed to model the impulse response as a sum of exponentially decaying sinusoids in the time domain. Bayesian model selection is applied to estimate the appropriate number of modes in the model. Bayesian parameter estimation determines the amplitude, decay time, and modal frequency of each mode. The Bayesian analysis is performed using a nested sampling approach to approximate the evidence for each candidate model. Results from the analysis are verified by a Fourier analysis of the experimentally measured data, and also with classical modal theory. Additional experimental measurements are performed to validate individual modal parameter estimates. The likelihood landscape for the selected model is further explored by uniformly sampling near the point of convergence at the end of nested sampling. Animations are used to observe transient behavior of the sample population throughout the analysis.