Improving the Convolutional Formulation for Efficient Computations of Short-Length DHT

Abstract

The implementation of the fast Hartley transform (FHT) of arbitrary sizes on various computer platforms is in demand in many application areas. The synthesis of fast algorithms for the discrete Hartley transform (DHT) based on cyclic convolutions requires the formation and improvement of the block-cyclic structure of the basis to reduce computational complexity. A compact description of the block structure of the basis of the DHT in the form of a cyclic decomposition of substitution is considered. The synthesis of algorithms is illustrated through the example of the convolutional formation of the improved block-cyclic structure of a 14-point DHT. Two different improving block-cyclic structures of the 21-point DHT and their average time of execution are represented. The analysis of block structures for the DHT, in which each cyclic block is processed either independently or as part of a larger cyclic structure, leads to a more efficient implementation of the transform. The advantage in computation speed for short FHTs on modern computer platforms is confirmed by the obtained results in comparison with the FFTW library.