Signal processing for transient acoustic fields

This paper discusses specific signal processing issues encountered in the development of Transient Near-field Acoustical Holography (TNAH). TNAH was recently presented as an innovation to carry out Nearfield Acoustical Holography (NAH) on short transient fields, such as impact noise. This specific NAH formulation uses a Laplace transform in the time domain instead of a Fourier transform, therefore reducing time aliasing problems. It is used both in forward and backward propagation as a non-contact technique for time and space visualization of both sound pressure field and transverse acceleration of the source. The present paper focuses on signal processing requirements to propagate transient sound fields, both forward and backward. Issues such as time aliasing and wraparound errors in Fourier based NAH are presented. The principles and features of the transient signal processing with the Laplace transform are defined. In forward propagation, windowing is required both in the space and frequency domains. In backward propagation, a double regularization process is also required in the k-space and the frequency domain. Transient sound fields radiated by impacted plates are processed. Compared to NAH, the error with TNAH is reduced by more than a factor of 10 without adding trailing zeros to the initial signals. The Laplace formulation could be applied to other holographic techniques.