A Split Vector-Radix Algorithm for the 3-D Discrete Hartley Transform

In this paper, we propose a three-dimensional (3-D) split vector-radix fast Hartley transform (FHT) algorithm. The main idea behind the proposed algorithm is that the radix-2/4 approach is introduced in the decomposition of the 3-D discrete Hartley transform by using an appropriate index mapping and the Kronecker product. This provides an algorithm based on a mixture of radix-(2times2times2) and radix-(4times4times4) index maps and has a butterfly that is characterized by simple closed-form expressions. This algorithm offers substantial reductions in the numbers of multiplications, additions, data transfers, and twiddle factor evaluations or accesses to the look-up table, without a significant increase in the structural complexity compared to that of the existing 3-D vector radix FHT algorithm