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Designing a Microphone Array for Acoustical Inverse Problems  

Kim, Youngtea (Computational Science ＆ Engineering Lab, Samsung Advanced Institute of Technology (SAIT))
Publication Information
The Journal of the Acoustical Society of Korea / v.23, no.1E, 2004 , pp. 3-9 More about this Journal
Abstract
An important inverse problem in the field of acoustics is that of reconstructing the strengths of a number of sources given a model of transmission paths from the sources to a number of sensors at which measurements are made. In dealing with this kind of the acoustical inverse problem, strengths of the discretised source distribution can be simply deduced from the measured pressure field data and the inversion of corresponding matrix of frequency response functions. However, deducing :he solution of such problems is not straightforward due to the practical difficulty caused by their inherent ill-conditioned behaviour. Therefore, in order to overcome this difficulty associated with the ill-conditioning, the problem is replaced by a nearby well-conditioned problem whose solution approximates the required solution. In this paper a microphone array are identified for which the inverse problem is optimally conditioned, which can be robust to contaminating errors. This involves sampling both source and field in a manner which results in the discrete pressures and source strengths constituting a discrete Fourier transform pair.
Keywords
Acoustical inverse problem; Condition number; Discrete Fourier transform;
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