Unidimensional and bidimensional prolate spheroidal wave functions and applications (Q647998)

The author gives a brief description of the theory and the properties of the 1-D and 2-D prolate spheroidal wave functions (PSWFs). Then, he studies some efficient methods for the computation of the different PSWFs and their associated eigenvalues. More precisely, he develops a quadrature method for the approximation of the 1-D PSWFs. Then, he extends this method to the construction of 2-D PSWFs that are concentrated on the unit disk. Also, he gives a brief review of the quality of approximation of almost band-limited functions by 1-D PSWFs. Moreover, he uses some numerical tests to compare between PSWFs and wavelets as signal processing tools. In particular, he gives some numerical tests that highlight the efficiency of PSWFs in processing band-limited signals.