Spatial impulse responses from a flexible baffled circular piston

The theory of orthogonal polynomial (Zernike) expansions of functions on a disk, as used in the diffraction theory of optical aberrations, is applied to obtain (semi-) analytical expressions for the spatial impulse responses arising from a non-uniformly moving, baffled, circular piston. These expres...

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Bibliographic Details
Published in:The Journal of the Acoustical Society of America 2011-05, Vol.129 (5), p.2952-2959
Main Authors: Aarts, Ronald M., Janssen, Augustus J. E. M.
Format: Article
Language:English
Subjects:
Acoustics
Bessel functions
Disks
Exact sciences and technology
Exact solutions
Fundamental areas of phenomenology (including applications)
Impulses
Mathematical analysis
Physics
Pistons
Series (mathematics)
Transduction
acoustical devices for the generation and reproduction of sound
Zernike polynomials
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Summary:The theory of orthogonal polynomial (Zernike) expansions of functions on a disk, as used in the diffraction theory of optical aberrations, is applied to obtain (semi-) analytical expressions for the spatial impulse responses arising from a non-uniformly moving, baffled, circular piston. These expressions are in terms of the expansion coefficients of the non-uniformity and the responses of the orthogonal expansion functions. The latter impulse responses have a closed form as finite series involving the Legendre functions and the sinc function. The method is compared with a similar method, proposed by P. R. Stepanishen [ J. Acoust. Soc. Am. 70 , 1176-1181 ( 1981 ) ] where zeroth order orthogonal Bessel functions, rather than Zernike polynomials, are used as expansion functions.
ISSN:0001-4966
1520-8524
DOI:10.1121/1.3562558