Estimating the dynamic range of music signals via random subsampling

The dynamic range is an important parameter which measures the spread of sound power. For music signals it is a measure of recording quality. There are various descriptive measures of sound power, none of which has strong statistical foundations. We start from a nonparametric model for sound waves where an additive stochastic term has the role to catch transient energy. The distribution of the variance of the stochastic term is used to measure the dynamic range. The stochastic component accommodates both short range dependence, and long range dependence. This component is recovered by a simple rate-optimal kernel estimator. The distribution of its variance is approximated by a consistent random subsampling method that is able to cope with the massive size of the typical dataset. Based on the latter, we propose a statistic that is able to represent the dynamic range concept consistently.