Dual algorithms for fast calculation of the Fourier-Bessel transform

This paper presents a new procedure for the fast calculation of the Fourier-Bessel transform. The computation is performed in a "dual" mode and involves two matched algorithms, the first of which provides the lower order components while the second yields intermediate and higher order samples of the transform. The first algorithm is based on the Fourier-selection-summation (FSS) method derived in a previous study, while the second relies on the Bessel function large argument asymptotic expansion. It is shown that the dual procedure constructed along these lines requires a computation time which is about four times that needed by a single N point fast Fourier transform.