Two-band fast Hartley transform

This article has been made available through the Brunel Open Access Publishing Fund.Efficient algorithms have been developed over the past 30 years for computing the forward and inverse discrete Hartley transforms (DHTs). These are similar to the fast Fourier transform (FFT) algorithms for computing the discrete Fourier transform (DFT). Most of these methods seek to minimise the complexity of computations and or the number of operations. A new approach for the computation of the radix-2 fast Hartley transform (FHT) is presented. The proposed algorithm, based on a two-band decomposition of the input data, possesses a very regular structure, avoids the input or out data shuffling, requires slightly less multiplications than the existing approaches, but increases the number of additions

On quaternary complex Hadamard matrices of small orders

One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are members of only a handful of parametric families, and each inequivalent matrix, up to transposition, can be identified through its fingerprint.Comment: 7 page