Computation of the Hankel transform using projections

In this paper two new algorithms for computing an nth-order Hankel transform are proposed. The algorithms are based on characterizing a circularly symmetric function and its two-dimensional Fourier transform by a radial section and interpreting the Hankel transform as the relationship between the radial section in the two domains. By utilizing the property that the projection of a two-dimensional function in one domain transforms to a radial section in the two-dimensional Fourier transform or inverse Fourier transform domain, several efficient procedures for computing the Hankel transform exploiting the one-dimensional FFT algorithm are suggested.