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

A New Parametric DFT-Based OFDM Transceiver for Intrinsic Wireless Communication Encryption

In this paper, we propose a parametric OFDM transceiver for wireless communication encryption. One of the major contributions of this work is the intrinsic encryption nature of the proposed system, since it is a completely new idea and philosophically different from the concept of existing secured OFDM systems requiring separate encryption blocks. The main idea behind the proposed system is the appropriate use of the parametric discrete Fourier transform (DFT-alpha) and its inverse IDFT-alpha, where alpha is randomly obtained from [-2pi, 0], to implement the OFDM system and at the same time inherently encrypt the communications. Thus, the resulting (IDFT-alpha/DFT-alpha)-based OFDM transceiver, which has a performance similar to that of the conventional IDFT/DFT-based OFDM transceiver, is applied and implemented in the IEEE 802.11a WIFI system framework OFDM for communication encrypting. Moreover, using BER and SNR, we experimentally determine the appropriate intervals of the possible values of alpha for perfect encryption in a flat fading channel assumed for optimal testing environment. We also examine and assess the effects of DFT-alpha on the transformation of the constellation pattern of the transmitted signal to prove the validity of the obtained intervals for different modulation schemes such as BPSK, QPSK, 16QAM, and 64QAM