Scale-free and characteristic time in urban soundscape

Abstract

In this work we study the statistic of the nocturnal and diurnal urban soundscape. Our focus is on the temporal distribution of the quiet-times (background noise) and sound-times (noise bursts) in audio recordings. We analyzed one hour samples uninterruptedly of urban environment soundscape for ten days and nights. The histogram for the nocturnal quiet-time follows a power-law like scale-free distribution spanning three orders of magnitude, from 0.03s to 30s, with exponent α=1.65±0.03. The diurnal histogram distributions of the quiet-times reveals a power-law with the same exponent value, but the statistic distribution, in this case, shows an overlap of an additional urban acoustic phenomenon corresponding to time duration above 1s. On the other side, the sound-times, both diurnal and nocturnal, follow a log-normal distribution with mean value around 0.1s, which characterizes a typical temporal characteristic-scale for the duration of sounds in the urban soundscape. We discuss, in the paper, the coexistence between the scale-free distribution of silences and the typical time scale of sounds.