New Formulation of Fast Discrete Hartley Transform with the Minimum Number of Multiplications

The discrete Hartley transfom(DHT) is a real-valued tratufom closely related to the discrete Fourier transform (OFT) of a real-valued sequence. It directly maps a rea[-valued sequence to a real-valuedspectrum while preserving some usefulproperties of the Dkcrete Fourier Transfom. In such case, the Discrete Hartley transform can act as an altemative form to the Fourier Tradorm for avoiding complex arithmetic, hence it becomes a valuable tool in digital signalprocessing. In this paper, a simple algorithm is proposed to realize one-dimensional DHT with sequence lengths equal to 2“‘. This algorithm achieves the same multiplicative complaity as Malvar’s algorithm which requires the minimum number of multiplications reported in the literature. However, the present approachgives the advantage of requiring a smallernumber of additions compared with the number that required in Malvar’s algorithm.