Sound visualization by using enhanced planar acoustic holographic reconstruction

Abstract

Acoustic holographic method is one of the most valuable sound visualization techniques for expressing sound with respect to time and space. This expression is directly related to the number of measurement points. The more one uses, the better quality one expects to have. This dissertation aims to develop methods which can enhance the quality of this expression for the given number of microphones. The planar acoustic holography has been chosen to be analyzed for this purpose. We assume that other types of acoustic holography such as cylindrical and spherical ones can be seen as a simple extension of planar acoustic holographic theory. For these purposes, the planar acoustic holographic method has been formulated in discrete domain to explore everything associated with realistic holographic reconstruction; spatial sampling error, wraparound error, and things related with finite aperture. Based on this work, the errors which degrade the reconstructed pictures of sound were thoroughly investigated. First, the effect of sampling in time and space was studied. The aliasing problem was investigated. The filtering technique to avoid this problem was studied. A modified spatial filter including the criteria for the near-field measurement condition and the far-field measurement one, were introduced. In the discrete holographic expression, the wraparound error is formulated. This error is induced by the finite dimension of the propagator tensor; in other words, by the circular convolution which is inherent in Fourier transform. The increase in the dimension of the propagator tensor reduces the error. At the same time the dimension of hologram matrix must be increased by adding zeros to equalize the dimension of the propagator tensor and the hologram matrix. Also rigorous analysis on truncation error has been performed. An effort to reduce the truncation error led to the development of two new techniques which are the two most important achievements in this dissertation. T...