A Fast Algorithm for Computation of General Integer-Order Hankel Transforms

The letter presents an improved algorithm for computation of general integer-order Hankel transforms, which is back-projection based. The original algorithm breaks the Hankel transform into an inverse fast Fourier transform and a discrete summation involving trigonometric terms (which is more computationally intensive). In this work, by varying the number of terms of the discrete summation with the transform order, the number of trigonometric computations and multiplications can be reduced drastically, which leads to overall computational complexity improvement. To be precise, the time complexity constant is reduced so much that our algorithm is faster than the state-of-the-art, while being O(N²). The algorithm has been simulated in MATLAB and a performance improvement of 6.04x in the discrete summation step (average case) over the original algorithm has been obtained. Finally, computational error of our proposed algorithm has been obtained, which is better than the baseline algorithm, and is comparable to the state-of-the-art.