Trans-dimensional Bayesian approaches to room acoustic modal analysis

Abstract

Bayesian approaches to room acoustic modal analysis offer a framework to identify numerous decaying modes in an impulse response. Typical Bayesian analysis requires two distinct steps: model selection and parameter estimation. Trans-dimensional approaches combine these steps. Model dimensionality itself becomes a parameter, and the analysis is performed via parameter estimation.

This work implements both fixed-dimensional and trans-dimensional nested sampling algorithms to analyze impulse responses and determine their modal content. Impulse responses are simulated using the Prony Model to capture amplitude, decay time, frequency and phase for each room mode. Experimental measurements are performed within the test chamber in two different configurations to compare results from each scenario. After performing initial analyses to determine modal frequencies additional measurements are performed to determine decay times at the frequencies identified. Decay times resulting from the Bayesian analyses of the measured impulse responses agree well with experimentally measured values from the test chamber. Numerous observations of the algorithmic behavior of the analyses are made. Ultimately, this work presents a first investigation into trans-dimensional nested sampling for room acoustic modal analysis. Numerous avenues for further exploration are discussed.