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.

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 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.