(19) * << * >> * Russian * English * Content * All Issues
А finite series approximation of spheroidal wave functions
S.N. Khonina
Image Processing Systems Institute of RAS
PDF, 640 kB
Pages: 65-70.
Full text of article: Russian language.
Abstract:
The article considers the approximation of elongated spheroidal functions by finite series and proposes a method for calculating the coefficients of such series. The paper provides a numerical performance analysis of the invariance property of elongated spheroidal zero-order functions in relation to an integral transformation with a sinc-kernel on a symmetric bounded interval.
Citation:
Khonina SN. А finite series approximation of spheroidal wave functions. Computer Optics; 1999; 19: 65 – 70.
References:
- D. Slepian, H.O. Pollak, Prolate spheroidal wave functions. Fourier Analysis and Uncertainty – I, The Bell System Technical Journal, 1961, 40, p.43-46.
- D. Slepian, Some asymptotic expansions for prolate spheroidal wave functions, J. Math. & Phys., 1965, 44, p. 99-140
- H.J. Landau, H.O. Pollak, Prolate spheroidal wave functions. Fourier Analysis and Uncertainty – II, The Bell System Technical Journal, 1961, 40, p.65-84.
- Khurgin YI, Yakovlev VP. Methods of the theory of entire functions in radio physics, communications theory, and optics. Moscow: Fizmatgiz; 1962.
- D. Slepian, Prolate spheroidal wave functions. Fourier Analysis and Uncertainty – IV: Extensions to many dimensions; generalized prolate spheroidal functions, The Bell System Technical Journal, 1964, 43, p.3009-3057.
- Montgomery W.D., Algebraic formulation of diffraction applied to self-imaging, J. Opt. Soc. Am., 58(8), 1112-1124 (1968).
- Koblyansky YV, Kurashov VN. Application of the method of eigenfunctions of optical systems for the statistical analysis of speckle pictures, Optika i Spectroscopiya; 1984; 57(4): 708-710.
- Lowan A. Spheroidal wave functions in Reference book on special functions edited by Abramovits M, Stigan I. Moscow: Nauka Publisher; 1979: 832.
- D. Slepian, E. Sonnenblick, Eigenvalues associated with prolate spheroidal wave functions of zero order, The Bell System Technical Journal, 1965, 44, p.1745-1763.
- Komarov IV, Ponomarev LI, Slavyanov SY. Spheroidal and coulombian spheroidal functions. Moscow: Nauka Publisher; 1976
- Flammer K. Tables of spheroidal wave functions, Vych. Tsentr Akad. Nauk SSSR; Moscow; 1962.
© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20