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Alternative discretizations for the numerical evaluation of Rayleigh’s integral based on Fourier acoustics

Authors Pagavino, M.
Year 2019
Thesis Type Audio Engineering project
Topic Audio Signal Processing
Keywords acoustic holography
Abstract This audio engineering project deals with the numerial evaluation of sound fields from plane radiators, based on the spatial Fourier method. By the means of the fast Fourier transform it is possible to evaluate the Rayleigh integral at high computational efficiency, a feature that made the near field holography popular in its beginnings. Nowaday, efficiency of the implementation is not a pre-requisite anymore, but it could potentially be advantageous, therefore it is reconsidered in this work. The calculation in via the discrete wave-number domain implies: (i) by the discretization of the propagator, waves propagating in parallel to the radiating plane get singular at some frequencies, and (ii) the inherent spatial periodization of the sound source affects the waves propagating into directions inclined with regard to the plane by interference. The work shows up possible strategies to mitigate these effects. As a thinkable remedy concerning the singularity, a rectangular or triangular interpolant is proposed in 2D, and a trapezoidal one in 3D. The results of FFT-based holography are compared with the correct results of the discretized Rayleigh integral. Moreover, the effects of the alternative discretization interpolants are investigated concerning the inverse holographic problem. The results provided justify the question if, from today's perspective, the FFT-based nearfield acoustic holography is still meaningful, compared to the Rayleigh integral discretized in the space domain.
Supervisors Zotter, F.