Fast evaluation of the Rayleigh integral and applications to inverse acoustics

Jelmer Wind, Ysbrand H. Wijnant, Andries de Boer

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In this paper we present a fast evaluation of the Rayleigh integral, which leads to fast and robust solutions in inverse acoustics. The method commonly used to reconstruct acoustic sources on a plane in space is Planar Nearfield Acoustic Holography (PNAH). Some of the most important recent improvements in PNAH address the alleviation of spatial windowing effects that arise due to the application of a Fast Fourier Transform to a finite spatial measurement grid. Although these improvements have led to an increase in the accuracy of the method, errors such as leakage and edge degradation can not be removed completely. Such errors do not occur when numerical models such as the Boundary Element Method (BEM) are used.Moreover, the forward models involved converge to the exact solution as the number of elements tends to infinity. However, the time and computer memory needed to solve these problems up to an acceptable accuracy is large. We present a fast (O(n log n) per iteration) and memory efficient (O(n)) solution to the planar acoustic problem by exploiting the fact that the transfer matrix associated with a numerical implementation of the Rayleigh integral is Toeplitz. In this paper we will address both the fundamentals of the method and its application in inverse acoustics. Special attention will be paid to comparison between experimental results from PNAH, IBEM and the proposed method.
Original languageUndefined
Number of pages8
Publication statusPublished - 2006
Event13th International Congress on Sound and Vibration, ICSV 2006 - Vienna, Austria
Duration: 2 Jul 20066 Jul 2006
Conference number: 13


Conference13th International Congress on Sound and Vibration, ICSV 2006
Abbreviated titleICSV


  • IR-58885

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