Affiliations: Department of Quantum Chemistry, Uppsala University, Box 518. S-751 20 Uppsala, Sweden. E-mail: [email protected]
Note: [1] Supported by the Royal Swedish Academy of Sciences, project number 12523, and the Russian Foundation for Basic Research under Grant No. 99-01-00331.
Note: [2] Permanent address: Department of Numerical Methods Computing Center of Russian Academy of Sciences Vavilova str.40, 117967 Moscow GSP-1, Russia, E-mail: [email protected]
Abstract: The general interest, in computing prolate spheroidal wave functions is discussed from the original practice of solving various problems in mathematical physics via separation of variables to more recent applications in signal processing. In particular we focus on the zero-order prolate spheroidal case where the actual functions are simultaneously eigenfunctions to the finite Fourier transform. Detailed considerations on the computational schemes are given and motivated. Earlier powerful developments of the Russian Computation School lead by Alexander Abramov are modified and simplified. Although the present technique in particular is restricted to the prolates it may be applicable to more general situations.
Keywords: Prolate spheroidal wave functions, finite Fourier transform, signal processing
