Wavelet-based non-stationary near-field acoustical holography

Near field acoustical holography (NAH) consists in reconstructing the pressure field radiated by a set of sources from the measurements received by a microphone array. Originally developed for stationary sound fields, this technique is widely used in the transportation industry where many sources are actually non-stationary. The purpose of this paper is to extend NAH so as to characterize non-stationary sources in the spatial as well as the time domains. To this end, a new approach is developed based on the inversion of the Helmholtz integral equation in a time-frequency wavelet basis instead of the usual Fourier basis. Source signals are directly reconstructed in fractional-octave-bands, which results in significant computational time saving by avoiding the inverse Fourier transform of a very large set of frequency bins. The inverse problem is defined by the relation existing between the wavelet coefficients of the source and those of the measured pressure fields, which is then solved with Monte-Carlo simulations. Numerical and experimental results finally illustrate the efficiency of the proposed approach.