Derivation of the Regularized Fast Hartley Transform

Abstract

This chapter discusses a new formulation of the FHT, referred to as the regularized FHT, which overcomes the limitations of existing FHT algorithms given the ultimate objective of mapping the solution onto silicon-based parallel computing equipment. A generic version of the double-sized butterfly, the GD-BFLY, is described which dispenses with the need for two sizes – and thus two separate designs – of butterfly as required via conventional fixed-radix formulations. Efficient schemes are also described for the storage, accession and generation of the trigonometric coefficients using suitably defined LUTs. A brief complexity analysis is then given in relation to existing FFT and FHT approaches to both the real-data and complex-data DFT problems. A discussion is finally provided relating to the results obtained in the chapter.