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Improvement in localization of planar Acoustic Holography

Authors Schmidt, P.
Year 2012
Thesis Type Master's thesis
Topic Audio Signal Processing
Keywords acoustic near-field holography, Rayleigh integral, sparsity, L1-Norm Minimization
Abstract To describe a soundfield in planar nearfield holography it is mathematically sufficient to know the boundary values. Inverse equations can be set up to trace back the sound waves to their source, based on measurements of the sound pressure. Available techniques are based on solutions of the Helmholtz equation or the Helmholtz integral equation and are frequently applied in noncontact measurement scenarios. These are, for in- stance, the wave superposition method (WSM), Helmholtz equation least squares (HELS), inverse boundary element method (IBEM), nearfield acoustic holography (NAH) or the statistically optimized NAH (SONAH). All these approaches have a tendency to be numerically ill-posed and are usually treated using the classical l2 -norm based system inversion techniques. How to deal with spatial aliasing, boundary wrap-around and loss or numerical instability is well discussed, however, available literature does not excessively address the poor point localization of these techniques. In this thesis, the mapping properties of l1 -optimized planar holography is discussed and compared with l2 -optimized calculation. To reveal different types of algorithmic behavior, a simulation of the soundfield is calculated for different types of sources.
Supervisors Zotter, F.