[Show abstract][Hide abstract] ABSTRACT: Near-field acoustic holography is a measuring process for locating and characterizing stationary sound sources from measurements made by a microphone array in the near-field of the acoustic source plane. A technique called real-time near-field acoustic holography (RT-NAH) has been introduced to extend this method in the case of nonstationary sources. This technique is based on a formulation which describes the propagation of time-dependent sound pressure signals on a forward plane using a convolution product with an impulse response in the time-wavenumber domain. Thus the backward propagation of the pressure field is obtained by deconvolution. Taking the evanescent waves into account in RT-NAH improves the spatial resolution of the solution but makes the deconvolution problem "ill-posed" and often yields inappropriate solutions. The purpose of this paper is to focus on solving this deconvolution problem. Two deconvolution methods are compared: one uses a singular value decomposition and a standard Tikhonov regularization and the other one is based on optimum Wiener filtering. A simulation involving monopoles driven by nonstationary signals demonstrates, by means of objective indicators, the accuracy of the time-dependent reconstructed sound field. The results highlight the advantage of using regularization and particularly in the presence of measurement noise.
The Journal of the Acoustical Society of America 06/2011; 129(6):3777-87. DOI:10.1121/1.3586790 · 1.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Near-field acoustic holography (NAH) is an effective tool for visualizing acoustic sources from pressure measurements made in the near-field of sources using a microphone array. The method involving the Fourier transform and some processing in the frequency-wavenumber domain is suitable for the study of stationary acoustic sources, providing an image of the spatial acoustic field for one frequency. When the behavior of acoustic sources fluctuates in time, NAH may not be used. Unlike time domain holography or transient method, the method proposed in the paper needs no transformation in the frequency domain or any assumption about local stationary properties. It is based on a time formulation of forward sound prediction or backward sound radiation in the time-wavenumber domain. The propagation is described by an analytic impulse response used to define a digital filter. The implementation of one filter in forward propagation and its inverse to recover the acoustic field on the source plane implies by simulations that real-time NAH is viable. Since a numerical filter is used rather than a Fourier transform of the time-signal, the emission on a point of the source may be rebuilt continuously and used for other post-processing applications.
The Journal of the Acoustical Society of America 12/2010; 128(6):3554-67. DOI:10.1121/1.3504656 · 1.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The aim of this work is to continuously provide the acoustic pressure field radiated from nonstationary sources. From the acquisition in the nearfield of the sources of a planar acoustic field which fluctuates in time, the method gives instantaneous sound field with respect to time by convolving wavenumber spectra with impulse response and then inverse Fourier transforming into space for each time step. The quality of reconstruction depends on the impulse response which is composed of investigated parameters as transition frequency and propagation distance. Sampling frequency also affects errors of the practically discrete impulse response used for calculation. To avoid aliasing, the impulse response is low-pass filtered with Chebyshev or Kaiser-Bessel filter. Another approach to implement the impulse response consists of applying an inverse Fourier transform to the theoretical transfer function for propagation. To estimate the performance of each processing method, a simulation test involving several source monopoles driven by nonstationary signals is executed. Some indicators are proposed to assess the accuracy of the temporal signals predicted in a forward plane. The results show that the use of a Kaiser-Bessel filter numerically implemented or that of the inverse Fourier transform can provide the most accurate instantaneous acoustic signals.
The Journal of the Acoustical Society of America 11/2009; 126(5):2367-78. DOI:10.1121/1.3216916 · 1.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The patch holography method allows one to make measurements on an extended structure using a small microphone array. Increased attention has been paid to the two techniques, which are quite different at first glance. One is to extrapolate the pressure field measured on the hologram plane while the other is to use statistically optimized processing. A singular value decomposition formulation of the latter is proposed in this paper. The similarity of the two techniques is shown here. Both use a convolution of the measured pressure patch to obtain a better estimate of the wavenumber spectrum backward propagated on the structure. By using the Morozov discrepancy principle to compute the regularization parameter, the two methods lead to very close results.
The Journal of the Acoustical Society of America 10/2009; 126(3):1264-8. DOI:10.1121/1.3192349 · 1.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Real-Time Nearfield Acoustic Holography (RT-NAH) reconstructs fluctuating sound fields due to non stationary sources by taking into account the evanescent waves. The signal received by the microphone array is processed in the time-wavenumber domain to obtain a continuous source signal on the reconstruction plane. The processing uses a convolution product with a transfer function of an inverse filter in the time-wavenumber domain. Taking the evanescent waves into account improves the spatial resolution of solutions but makes the deconvolution problem ”illposed”. Thus, the inverse of the transfer function is neither unique nor stable. A regularization method is used to solve this problem by giving another constraint. In our case the standard Tikhonov regularization is used, which is based on the minimisation of the energy solution, combined with generalized crossed validation to estimate the regularization parameters. This method leads to a time dependent pressure distribution on the source plane in order to localize and characterize the different sound sources.
[Show abstract][Hide abstract] ABSTRACT: Real-Time Nearfield Acoustic Holography (RT-NAH) is a method to reconstruct fluctuating sound fields due to non stationary sources. This technique takes into account the evanescent waves for the reverse propagation and consequently leads to a good resolution at low frequencies. The signal received by the microphone array is processed in the time-wavenumber domain to obtain a continuous source signal on the reconstruction plane. The processing method uses the convolution of each point of the instantaneous wavenumber spectrum by an inverse filter. In previous work, the computation of the inverse filter was made from the impulse response based on the analytical solution of the direct propagation equation. In this paper, a new technique is tested for the reverse propagation in the time-wavenumber domain using the Finite-Difference Time-Domain (FDTD) method. Stability and dispersion effects are analysed. Results show the validity of this approach to construct the inverse filter of RT-NAH.
[Show abstract][Hide abstract] ABSTRACT: The aim of the study is to demonstrate that some methods are more relevant for implementing the Real-Time Nearfield Acoustic Holography than others. First by focusing on the forward propagation problem, different approaches are compared to build the impulse response to be used. One of them in particular is computed by an inverse Fourier transform applied to the theoretical transfer function for propagation in the frequency-wavenumber domain. Others are obtained by directly sampling an analytical impulse response in the time-wavenumber domain or by additional low-pass filtering. To estimate the performance of each impulse response, a simulation test involving several monopoles excited by non stationary signals is presented and some features are proposed to assess the accuracy of the temporal signals resulting from reconstruction processing on a forward plane. Then several inverse impulse responses used to solve the inverse problem, which consists in back propagating the acoustic signals acquired by the microphone array, are built directly from a transfer function or by using Wiener inverse filtering from the direct impulse responses obtained for the direct problem. Another simulation test is performed to compare the signals reconstructed on the source plane. The same indicators as for the propagation study are used to highlight the differences between the methods tested for solving the Holography inverse problem.
[Show abstract][Hide abstract] ABSTRACT: Near-field Acoustic Holography (NAH) [Maynard et Williams, 1985] is a measuring process for locating stationary sound sources from measurements made by an antenna of microphones positioned near the acoustic source plane. In order to characterize non-stationary sources, a new formulation has been introduced [Grulier, 2004] to propagate signals on a forward plane using a convolution product with an impulse response in the time-wavenumber domain. The purpose of this study is to solve the deconvolution problem in order to introduce the Real-Time Acoustic Holography and to test its accuracy. Taking the evanescent waves into account improves the spatial resolution of the solution but makes the deconvolution problem "ill-posed". Thus, the inverse of the impulse response is neither unique nor stable. Then, regularization methods that consist of giving an other constraint to the solution to solve this problem are studied. In particular, the standard Tikhonov regularization is used, which is based on the minimisation of the solution's energy, combined with generalized cross validation to estimate the regularization parameters. This method provides an image representation of the time dependent pressure of the source plane in order to localize and characterize the different sound sources.
The Journal of the Acoustical Society of America 06/2008; 123(5):3386. DOI:10.1121/1.2934038 · 1.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Instead of the generally named "time holography" techniques which operate in the frequency domain to process differently progressive and evanescent waves, the Real-Time Nearfield Acoustic Holography algorithm (RT-NAH) works in a time-wavenumber domain. Each point of the instantaneous wavenumber spectrum is convolved by an numerical filter. Thus, it is possible to continuously reconstruct the acoustic pressure field on the plane from where some non stationary sources radiate. The starting point is the acquisition, in the near-field of the sources, of a pressure field which fluctuates in time. Then a space Fourier transform is applied to each temporal sample of the whole antenna of microphones. An analytic study of the problem shows that the pressure field can be propagated on a forward plane by filtering it in the time-wavenumber domain. In order to backpropagating the pressure field to the source plane, the impulse response has to be inverted. The realization of the inverse numerical filter is reported. After filtering, the fluctuating pressure signal is obtained by computing the inverse space Fourier transform of each time sample of the instantaneous wavenumber spectrum rebuilt on the source plane.