Evaluation of the air particle velocity signal from the binaural pressure impulse response

Abstract

From the Lagrangian theory in linear acoustics one clearly infers that the generalized momenta of the sound field are the acoustic pressure and the three components of the air particle velocity. This means that only through the knowledge of the full set of these four quantities a complete physical identification of the sound field can be achieved. The binaural technology represents an important tool for this goal, since it offers a method for reconstructing the pressure sound field by means of a couple of pressure impulse responses measured in two close points. An additional improvement of the binaural signal processing can be obtained using the two pressure input signals for evaluating the velocity component along the direction determined by the measurement points. First the velocity impulse response component is evaluated by means of the Euler equation and then, by convolving this signal with the usual anechoic signal, the velocity is reconstructed. In this paper the rigorous mathematical procedure for accomplishing the above task is presented.