Matching Pursuit, a well-known technique used in audio decomposition and sparse representation, is applied to Room Impulse Responses (RIRs) in order to investigate some statistical foundations of Room Acoustics. The detection of arrivals and the estimation of mixing time are therefore possible. This study is a first step towards a validation of the ergodic theory of reverberation. The use of Matching Pursuit is implicit since correlation between the impulse response and the direct sound is assumed.
This presentation shows why the compensation of the energy decay of the RIR is necessary to obtain stationary signals, and also how to estimate the best temporal boundaries of the direct sound of the RIR. The choice of a stopping criteria, based on the similarity between acoustical indices of the original RIR and those of the reconstructed signal, is discussed.
The cumulative distribution functions of arrivals of experimental and synthesized RIRs (using a stochastic model, which is presented) are compared. The mixing time is estimated when the arrival density becomes constant. The dependance of mixing time upon the distance source/receiver is investigated with measured and synthesized RIRs. It is shown how the integration of the diffusion to the model improves the match between mixing times of experimental and synthesized RIRs.
Bio:Guillaume Defrance is a PhD student (supervised by Jean-Dominique Polack) at the Institut Jean Le Rond d'Alembert in the LAM team (previously the Laboratory of Musical Acoustics), at University Paris 6, France.
Guillaume obtained a Master degree of Physical Acoustics at the University Pierre et Marie Curie (Paris). Guillaume has investigated different topics in acoustics during his studies, such as: the physics of instruments (classic guitar), the reproduction of a soundfield in 3D (Wave Field Synthesis), and the study of the cross-cultural perception of urgent sounds.
His PhD concerns stochastic modeling of room acoutics. Guillaume has refurbished a software widely used in the room acoustics community (the OpenMIDAS package), studied the detection of onset of room impulse responses (RIRs), and investigated statistics of RIRs in order to estimate arrivals and the mixing time (among others).