Comment on ´Vector Hartley transform´

The vector Hartley transform algorithm was recently proposed for efficient transformation of real data by J.D. Villasenor and R.N. Bracewell. It maps a very long one-dimensional input into a multidimensional array by an index mapping. However, this index mapping results in a complicated expression; also, multiplying each element of the intermediate array by an appropriate factor is necessary. This ´Comment´ is to point out that these multiplications are unnecessary, and can be eliminated by a proper prime-factor mapping technique. The authors reply that the use of prime factor decomposition is well known in Fourier transformation as providing very efficient operation, and the same may be expected for the Hartley transform. The reduction of the argument of the cas function from three to two terms is clearly very helpful. However, the gain in speed is dependent on the prime factors that are chosen, and needs to be checked in a given environment by overall timing.