Investigation of transient near-field acoustical holography using temporal and spatial Laplace transforms

This paper discusses a method to reduce the error in near-field acoustical holography (NAH) applied to transient radiations by using time and space domains Laplace transforms. Impact noise in industrial environments is a significant cause of hearing impairments. In order to find ways to reduce its importance, NAH can be used to visualize radiated sound fields. However, the use of NAH for transient sound fields such as impact noise implies the calculation of direct and inverse space and time domain discrete Fourier transforms. This leads to significant time aliasing and spatial wraparound errors in the reconstructed signals. The purpose of this paper is thus to present an alternative method that suppresses or reduces both errors. The proposed method is a generalized formulation of transient near-field acoustical holography, which relies on the use of a numerical Laplace transform over the time domain as a replacement for the Fourier transform considered in standard NAH formulation. In the case of short transient fields, transient NAH suppresses time aliasing errors while wraparound errors are simply reduced by using a zero-padding, which considerably increases computing cost. As an enhancement to transient NAH, a 2D spatial Laplace transform is also considered to reduce wraparound errors for such transient fields. The resulting Laplace transform-based NAH formulation is compared to the standard NAH method. Simulated short-time radiation of a baffled circular piston is used in both methods to provide time and space reconstructed signals. The results show that the use of Laplace transforms in both space and time domains suppresses time aliasing and reduces spatial wraparound errors.