Quantifying sound-field diffuseness in small rooms using multifractals

Abstract

With the aim of quantifying sound-field uniformity in spaces of relatively low volume, four different configurations in terms of acoustic treatment and sound-field diffuseness were constructed and tested. In a diffuse sound field, reflections are not strongly correlated both to the original sound and to earlier reflections. The degree of correlation is embedded in the impulse response structure, but is not trivial to identify. The room impulse responses exhibit self-similarity and therefore may be treated as multifractal signals characterized by a singularity spectrum. The singularity spectrum contains a wealth of information about the acoustic field established in the room. The width of the singularity spectrum, in particular, is directly related to the complexity of the impulse response structure. The uniformity of the sound field in the room can be evaluated by examining the variation of the singularity spectra with position. A new definition for sound field diffuseness is given that is not based on the concept of the energy density. The proposed method is simple to apply, statistically robust, and provides a measure of diffusion independent of the room reverberation.