Fast algorithm for the computation of the zero-order Hankel transform

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Abstract
The Hankel transform may be defined as the two-dimensional Fourier transform of a circularly symmetric function. A new Hankel-transform algorithm based on this definition is described. The proposed algorithm efficiently generates a rectangularly sampled two-dimensional output array by using the circular symmetry properties of the input array and two-dimensional vector radix fast-Fourier transform techniques. It accomplishes this by partitioning the input matrix into smaller and smaller processing blocks while removing redundant blocks from data manipulations. For applications that require the output data to be sampled on a two-dimensional rectangular raster, the convenience and the computational speed of the resulting algorithm offer advantages over the one-dimensional Hankel-transform algorithms currently available.

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