Separation of nonstationary sound fields in the time-wavenumber domain.

A number of sound field separation techniques have been proposed for different purposes. However, these techniques just consider the separation of sound fields in the space domain and are restricted to stationary sound fields. When the sound fields are nonstationary, it is also necessary to perform the separation in the time domain. Therefore, on the basis of the propagation principle of sound pressure in the time-wavenumber domain, a nonstationary sound field separation technique with two closely spaced parallel measurement surfaces is proposed. It can separate the nonstationary signals generated by the primary sources in both time and space domains when the disturbing sources exist on the other side of the measurement plane. The signals in time and space domains are separated by using the spatial Fourier transform method and the time domain deconvolution method. A simulation involving two monopoles driven by nonstationary signals demonstrates that the method proposed can remove the influence of disturbing sources in both time and space domains. The feasibility of this method is also demonstrated by an experiment with two loudspeakers located on two sides of measurement planes. Additionally, to comment more objectively on the separation results, some indicators are computed in both the simulation and experiment.

Reconstruction of nonstationary sound fields based on the time domain plane wave superposition method.

A time-domain plane wave superposition method is proposed to reconstruct nonstationary sound fields. In this method, the sound field is expressed as a superposition of time convolutions between the estimated time-wavenumber spectrum of the sound pressure on a virtual source plane and the time-domain propagation kernel at each wavenumber. By discretizing the time convolutions directly, the reconstruction can be carried out iteratively in the time domain, thus providing the advantage of continuously reconstructing time-dependent pressure signals. In the reconstruction process, the Tikhonov regularization is introduced at each time step to obtain a relevant estimate of the time-wavenumber spectrum on the virtual source plane. Because the double infinite integral of the two-dimensional spatial Fourier transform is discretized directly in the wavenumber domain in the proposed method, it does not need to perform the two-dimensional spatial fast Fourier transform that is generally used in time domain holography and real-time near-field acoustic holography, and therefore it avoids some errors associated with the two-dimensional spatial fast Fourier transform in theory and makes possible to use an irregular microphone array. The feasibility of the proposed method is demonstrated by numerical simulations and an experiment with two speakers.

Regularization for improving the deconvolution in real-time near-field acoustic holography.

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.

Patch near-field acoustic holography: regularized extension and statistically optimized methods.

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.

Forward propagation of time evolving acoustic pressure: formulation and investigation of the impulse response in time-wavenumber domain.

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.

On the statistical errors in the estimate of acoustical energy density by using two microphones in a one dimensional field.

It was recently shown that the statistical errors of the measurement in the acoustic energy density by the two microphone method in waveguide have little variation when the losses of coherence between microphones increase. To explain these intervals of uncertainty, the variance of the measurement is expressed in this paper as a function of the various energy quantities of the acoustic fields--energy densities and sound intensities. The necessary conditions to reach the lower bound are clarified. The results obtained are illustrated by an example of a one-dimensional partially coherent field, which allows one to specify the relationship between the coherence functions of the pressure and particle velocity and those of the two microphone signals.

2D full field vibration analysis with multiplexed digital holograms.

Opportunities for full field 2D amplitude and phase vibration analysis are presented. It is demonstrated that it is possible to simultaneously encode-decode 2D the amplitude and phase of harmonic mechanical vibrations. The process allows the determination of in plane and out of plane vibration components when the object is under a pure sinusoidal excitation. The principle is based on spatial multiplexing in digital Fresnel holography. Experimental results are presented in the case of an industrial application.

Full-field vibrometry with digital Fresnel holography.

A setup that permits full-field vibration amplitude and phase retrieval with digital Fresnel holography is presented. Full reconstruction of the vibration is achieved with a three-step stroboscopic holographic recording, and an extraction algorithm is proposed. The finite temporal width of the illuminating light is considered in an investigation of the distortion of the measured amplitude and phase. In particular, a theoretical analysis is proposed and compared with numerical simulations that show good agreement. Experimental results are presented for a loudspeaker under sinusoidal excitation; the mean quadratic velocity extracted from amplitude evaluation under two different measuring conditions is presented. Comparison with time averaging validates the full-field vibrometer.