A comparison of partial coherence and singular value partial field decomposition in the context of near-field acoustical holography

Abstract

Sound fields radiated by complex noise sources, e.g., automotive engines, generally comprise superposed individual fields generated by incoherent subsources. When applying near-field acoustical holography (NAH) to such fields it is first necessary to decompose the total sound field measured on the hologram plane into coherent partial fields, each of which is then projected to a reconstruction plane where they are summed on an energy basis. The partial field decomposition is performed after first calculating the cross spectra between a number of reference microphone signals that have been conditioned by using either partial coherence or singular value decomposition procedures, and the spatially sampled sound pressures on the hologram plane. That cross-spectral information then allows the partial fields to be created. In this presentation, the performance of the two reference signal decomposition procedures will be compared theoretically and experimentally. In particular, it will be shown that partial coherence decomposition allows the partial fields to be associated with the fields radiated by individual subsources if the latter are sufficiently separated spatially. In contrast, the singular value decomposition procedure usually results in partial fields that combine the properties of the subsources, and are thus not directly related to the fields radiated by individual subsources.