Room reflections analysis with the use of spherical beamforming and wavelets

Beamforming algorithms are widely used nowadays to localize sound sources in several types of environments. In general, the goal is to identify the direction from where a given signal is arriving. It consists of a spatial analysis performed over 2D maps, according to the frequency bands of interest or to a given spectral characteristic. In this paper, a spherical microphone array structure is developed. The signals obtained are input to Wavelet transform, in order to decompose impulse responses for real rooms. The objective is to extend the beamforming array capacity to identify and extract energy peaks from measured room impulse responses. The detected peaks represent sound reflections over the room surfaces, which can be used to describe acoustically the environment studied. With the proposed structure, it is possible to create acoustic maps, discretized in time and frequency, extending the applicability of traditional beamforming to provide directional impulse responses in reverberant spaces. The beamforming combines spherical harmonic decomposition with the Delay-and-Sum algorithm, whose result is post-processed through an Wavelet Transform. The system is applied to the array impulse response and allows to identify the incidence time and direction of the early reflections. The results are compared with those provided by ray-tracing simulation. A very good agreement is obtained for the detection of the first order reflections, besides the physical and spatial constraints of the spherical array developed.