Some New Results in Fast Hartley Transform Algorithms - M.S. Thesis

Finding the spectrum of a signal swiftly has been an ever-growing demand in Digital Signal Processing. In quest to meet this stipulation, Discrete Hartley Transform (DHT) is becoming as an encouraging substitute to the more popular discrete Fourier transform. Fast methods to compute the DHT are in existence and are named as fast Hartley transforms (FHTs). In this thesis, a new split-radix FHT algorithm for real-symmetric data, which discloses the dispensable computations, is developed. New radix-3, 6 and 12 FHT algorithms are derived with the help of an efficacious indexing scheme by pairing the rotating factors. When the needed number of Hartley transform samples is larger than the number of samples in the time-domain, a generalized input pruning procedure is prefaced to disjoin the undesirable computations in radix-2 decimation-in-frequency algorithm. Similarly, output pruning procedure is introduced in the context in which the required transform samples are fewer than the input samples. Finally, a generalized prefolding procedure, to find shape of the transformed sequence expeditiously but with fewer number of transform samples, is introduced at the input of the decimation-in-time (DIT) and decimation-in-frequency (DIF) FHT algorithms.