New radix-based FHT algorithm for computing the discrete Hartley transform

In this paper, a new fast Hartley transform (FHT) algorithm-radix-2
²
suitable for pipeline implementation of the discrete Hartley transform (DHT) is presented. The proposed algorithm is developed by integrating two stages of the twiddle factor decomposition together into single butterfly, and applying the multidimensional index mapping technique. Radix-2
²
algorithm achieves at the same time both a simple and regular butterfly structure as a radix-2 algorithm and a reduced number of twiddle factor multiplication provided by a radix-4 algorithm and, unlike radix-4, can be applied to any transform length that is power-of-two with simple bit reversing for ordering the output sequence. The algorithm performance is analyzed and the number of multiplications and additions are calculated. Furthermore, a method for reducing the number of multiplications and additions is proposed, making it possible to noticeably improve the arithmetic complexity as compared with the existing FHT algorithms.