New Efficient Algorithm for the Discrete Hartley Transform

Abstract

In real-time signal processing applications, the discrete version of the transform introduced by Hartley (DHT) has been proved to be an efficient substitute to the discrete Fourier transform (DFT). A new algorithm for fast calculations of the DHT (FHT) based on radix -2/4/8 method is introduced in this paper. In comparison with the split radix FHT algorithm, the proposed algorithm has a comparable arithmetic complexity, but preserves the regularity and the simple butterfly structure of the radix-2 algorithm. The development of the algorithm is motivated by firstly deriving a new radix-2/8 FHT algorithm and then cascading it with the radix-4 and radix-2 FHT algorithms. The arithmetic complexity of the developed algorithm has been implemented and analyzed by calculating the number of real additions and multiplications for different transform lengths. Comparisons with the existing FHT algorithms have shown that this algorithm can be considered as a good compromise between structural and arithmetic complexity.