Improving the Near-field Acoustical Holography Results by Using the Regressive Discrete Fourier Series

The planar Near-field Acoustical Holography (NAH) is a non-contact technique that can be used to estimate the vibration pattern of a planar body from the sound pressure it produces on a planar microphone array. The conventional NAH relies on the spatial Discrete Fourier Transform (DFT), requiring the microphone array to be larger than the source to reduce the spatial windowing effects due to the finite measurement aperture. This constraint can be overcome by “patch” NAH procedures, such as the Statistically Optimal NAH (SONAH). However, the patch algorithms are less efficient and differ significantly from the conventional NAH algorithm. As an alternative, this work proposes an improved Fourier-based NAH technique, which replaces the DFT by the Regressive Discrete Fourier Series (RDFS). Unlike the former, the latter lets the period of the Fourier series be larger than the measurement aperture, and the number of wavenumber components be smaller than the number of microphones. Then, the Fourier coefficients are obtained in the least-squares sense. Thus, by setting the period and the number of spectrum lines, a microphone array significantly smaller than the source can be used, which is shown in this paper through numerical simulations. Finally, the computation time and the algorithm structure of the DFT and RDFS-based NAH are similar; the only difference being the way the space-wavenumber transformation is done.