Fast Hankel transform by fast sine and cosine transforms: the Mellin connection

The Hankel transform of a function by means of a direct Mellin approach requires sampling on an exponential grid, which has the disadvantage of coarsely undersampling the tail of the function. A novel modified Hankel transform procedure that does not require exponential sampling is presented. The algorithm proceeds via a three-step Mellin approach to yield a decomposition of the Hankel transform into a sine, a cosine, and an inversion transform, which can be implemented by means of fast sine and cosine transforms.