New radix-3 and −6 decimation-in-frequency fast Hartley transform algorithms

Fast algorithms of a transform, like fast Fourier transform (FFT) algorithms, are based on different decomposition techniques. It is shown that these decomposition techniques can also be applied to the computation of the discrete Hartley transform (DHT) for a real-valued sequence. Recently, an efficient decomposition technique for radix-3 decimation-in-time (DIT) FFT and fast Hartley transform (FHT) algorithms has been demonstrated. Such a decomposition technique is implemented for radix-3 and -6 decimation-in-frequency (DIF) FHT algorithms and found to improve the operation count. Efficiency in these algorithms is derived by pairing the rotating factors with an appropriate reordering of the input sequence. From the results, it is seen that the radix-3 and -6 FHT algorithms presented are comparable to the split-radix FHT algorithm in terms of their operation count and will be more efficient when the sequence length is closer to an integer power of the corresponding radix.