A Statistical Method for Parameter Estimation from Shroeder Decay Curves

The sound decay curve, measured by either the interrupted noise method or the Schroeder method, can provide relevant information pertaining to a room's acoustical properties. However, the relevant information is not always readily extractable from the measurements. In this study, measurements of the decay curves of the historically important Vadstena Abbey church in Sweden have been obtained using both of the classical methods. The test building was in normal use with high levels of background noise during the measurements. A line-fit analysis showed a trend where the Schroeder decay curves yielded a longer estimated reverberation time compared to the interrupted noise method for low frequencies. This indicates that the measurement results are affected by background noise. A statistical model was developed for the Schroeder decay curve in such circumstances. Using it, the maximum likelihood estimates for the deterministic decay parameters can be found even when there are multi-slope decay patterns or significant background noise. The model is straight-forward to implement and can find an estimate for a single-slope decay also when some commercial software fails. The performance for double-slope decay models, as well as a comparison to the results from the interrupted noise method, are analyzed.