Direct split-radix algorithm for fast computation of type-II discrete Hartley transform

In this paper, a novel split-radix algorithm for fast calculation the discrete Hartley transform of type-II (DHT-II) is intoduced. The algorithm is established through the decimation in time (DIT) approach, and implementedby splitting a length N of DHT-II into one DHT-II of length N/2 for even-indexed samples and two DHTs-II of length N/4 for odd-indexed samples. The proposed algorithm possesses the desired properties such as regularity, inplace calculation and it is represented by simple closed form decomposition sleading to considerable reductions in the arithmetic complexity compared to the existing DHT-II algorithms. Additionally, the validity of the proposed algorithm has been confirmed through analysing the arithmetic complexityby calculating the number of real additions and multiplications and associating it with the existing DHT-II algorithms

New Decimation-In-Time Fast Hartley Transform Algorithm

This paper presents a new algorithm for fast calculation of the discrete Hartley transform (DHT) based on decimation-in-time (DIT) approach. The proposed radix-2^2 fast Hartley transform (FHT) DIT algorithm has a regular butterfly structure that provides flexibility of different powers-of-two transform lengths, substantially reducing the arithmetic complexity with simple bit reversing for ordering the output sequence. The algorithm is developed through the three-dimensional linear index map and by integrating two stages of the signal flow graph together into a single butterfly. The algorithm is implemented and its computational complexity has been analysed and compared with the existing FHT algorithms, showing that it is significantly reduce the structural complexity with a better indexing scheme that is suitable for efficient implementation

New fast Walsh–Hadamard–Hartley transform algorithm

This paper presents an efficient fast Walsh–Hadamard–Hartley transform (FWHT) algorithm that incorporates the computation of the Walsh-Hadamard transform (WHT) with the discrete Hartley transform (DHT) into an orthogonal, unitary single fast transform possesses the block diagonal structure. The proposed algorithm is implemented in an integrated butterfly structure utilizing the sparse matrices factorization approach and the Kronecker (tensor) product technique, which proved a valuable and fast tool for developing and analyzing the proposed algorithm. The proposed approach was distinguished by ease of implementation and reduced computational complexity compared to previous algorithms, which were based on the concatenation of WHT and FHT by saving up to 3N-4 of real multiplication and 7.5N-10 of real addition

Fast Algorithm for Computing the Discrete Hartley Transform of Type-II

The generalized discrete Hartley transforms (GDHTs) have proved to be an efficient alternative to the generalized discrete Fourier transforms (GDFTs) for real-valued data applications. In this paper, the development of direct computation of radix-2 decimation-in-time (DIT) algorithm for the fast calculation of the GDHT of type-II (DHT-II) is presented. The mathematical analysis and the implementation of the developed algorithm are derived, showing that this algorithm possesses a regular structure and can be implemented in-place for efficient memory utilization.The performance of the proposed algorithm is analyzed and the computational complexity is calculated for different transform lengths. A comparison between this algorithm and existing DHT-II algorithms shows that it can be considered as a good compromise between the structural and computational complexities