A bootstrap estimation of confidence levels in reverberation time measurements at low frequencies

Regular paper

Universidad de VIgo

Monday 1 june, 2015, 12:20 - 12:40

0.9 Athens (118)

Abstract:

In this job, a bootstrap evaluation of the confidence intervals in reverberation time measurement is
presented and discussed.
The usual way to obtain the coverage factor to obtain the confidence interval of the data set obtained from
a measurement is to calculate the standard deviation of the data and assume that the population is
normally distributed. It will be shown in this paper, how either multimodal or asymmetric probability
density functions are possible in reverberation time measurements at low frequencies. The sampling of the
acoustic space (i.e. the selection of microphone position), the filtering technique used (direct or reversed),
the modal density of the room and in the case of low modal density the value of the resonance frequencies,
will strongly influence the kind of probability density function. Therefore, it will be shown that the
assumption of normal distribution is no valid for reverberation time measurements at low frequencies. A
bootstrap based method to obtain confidence intervals for reverberation time measurements will be
described. The proposed method is validated by simulations and by using an extensive measurement
dataset of a room. Reasonably good confidence levels are reached in both cases. Good performance is
achieved because the bootstrap principle can model the periodicity of the energy distribution in the room,
so the proposed method is expected to work well in real measurements for most of the rooms. The
minimum number of microphone positions required o obtain an a good approximation of the confidence
levels of the reverberation time measurement is also presented.