Evaluation of reverberation times using a nonlinear regression approach

Abstract

Reverberation decay curves can be obtained by the backward integration of room impulse responses proposed by M. R. Schroeder. The evaluation of reverberation times is often achieved by a linear regression line fitting the reverberation decay curves. However, under noisy conditions, the successful application of this method requires either a careful choice of the integration limit or a precise estimate of the mean-square value of the background noise. In the present paper, an alternative method using a nonlinear iterative regression approach for evaluating reverberation times from Schroeder’s decay curves is proposed. A nonlinear model of the decay curves, established according to the nature of Schroeder’s decay curves, is used for the regression process rather than the linear model used in linear regression. The regression process is based on the generalized least-squares error principle in which a rapid convergence can be observed. Preliminary experiments show a slight dependence of the reverberation time T30 dB on both the integration limit and the background noise. Using this approach, a high precision of reverberation time evaluations can be achieved without either careful selection of the integration limit or precise estimation of the mean square value of the background noise.