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

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.

A comparison of the factorization approach to temporal and spatial propagation in the case of some acoustic waves

“…Further, each equation for the relevant wave field  ( ) g r t , has, on the right hand side (RHS), a term Q which represents some general source term. Typically [5,9] Q is an impulse designed to elicit the primitive response of the system (i.e. Q=Q δ(t)δ(x)), but here it is allowed to be any kind of perturbation, (non)linear modification, or driving term we desire.…”

Instantaneous Bayesian regularization applied to real-time near-field acoustic holography

“…with c being the celerity of the acoustical waves and Pðk x ; k y ; z; tÞ ¼ 0 for t < s, where s ¼ ðDzÞ=c is the propagation delay. The derivation of this equation leads to an analytical expression of the impulse response function, 23,24 hðk x ; k y ; Dz; tÞ ¼ hðX r ; s; tÞ ¼ dðt À sÞ À gðX r ; s; tÞ; (4) where dðsÞ is the Dirac function,…”

“…where hð:::; nDtÞ stands for the discretized version of the impulse response hð:::; tÞ. Sampling the impulse response causes phase and magnitude discrepancies, as mentioned by Grulier et al 24 They proposed corrections based on designing low-pass filters to overcome these difficulties by comparing the theoretical transfer function with the discrete Fourier transform of the impulse response. Another solution recommended 17,24 to reduce such errors is to replace direct sampling by average sampling, for instance, by using the trapezoidal formula g n…”

A Finite‐Difference Wavenumber‐Time Domain Method for Sound Field Prediction in a Uniformly Moving Medium

“…Compared with the frequency domain method, the time domain method has some advantages that the transient effects can be easily observed, and the response over a broad frequency range can be obtained with a single simulation run on condition that the excitation is given as a short acoustic pulse [11,12]. As for nearfield acoustic holography, it needs a known impulse response or green function in a moving medium, which can be specifically called real-time nearfield acoustic holography or time-domain equivalent source method, and in fact there is a distortion problem for impulse response sampling or an instability problem in iterative process to obtain equivalent source strength, respectively [7,13]. On the contrast, the FDTD method does not need the transfer relationships, and thus it has advantages of flexibility and conceptual simplicity.…”