Acoustical Holography for Non-Stationary Sources Using Orthogonal-Like Fractional Octave Band Filters

Abstract

The Fourier transform is suitable for analysis of stationary acoustic sources only. In contrast wavelet analysis provides information localized both in frequency and in time, which makes it highly appropriate for the study of non-stationary signals. Near field acoustic holography (NAH) is an experimental technique that makes it possible to reconstruct an image of the spatial acoustic field at one frequency, or in a frequency band, from pressure measurements returned by a microphone array. Several variants of NAH have been proposed to characterize non-stationary sources in time rather than in the domain. The idea of ​​this paper is to develop a new NAH method based on orthogonal-like wavelets that can achieve a fractional octave band analysis without relying on the Fourier transform. An inverse problem is posed with relates the wavelet coefficients of the source field to those of the measured pressure. This is then solved with Monte-Carlo simulations. Numerical and experimental results finally illustrate the efficiency of the proposed approach.