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

Polinomno filtriranje: postizanje bilo kojeg stupnja na nepravilno uzorkovanim podacima

Conventionally, polynomial filters are derived for evenly spaced points. Here, a derivation of polynomial filters for irregularly spaced points is provided and illustrated by example. The filter weights and variance reduction factors (VRFs) for both expanding memory polynomial (EMP) and fading-memory polynomial (FMP) filters are programmatically derived so that the expansion up to any degree can be generated. (Matlab was used for doing the symbolic weight derivations utilizing Symbolic Toolbox functions.) Order-switching and length-adaption are briefly considered. Outlier rejection and Cramer-Rao Lower Bound consistency are touched upon. In terms of performance, the VRF and its decay for the EMP filter is derived as a function of length (n) and the switch-over point is calculated where the VRFs of the EMP and FMP filters are equal. Empirical results verifying the derivation and implementation are reported.Polinomni filtri uobičajeno se rade za ravnomjerno raspoređene točke u prostoru. U ovom radu dana je derivacija polinomnih filtara za neravnomjerno raspoređene točke. Težinske vrijednosti filtra i faktori smanjenja varijance (VRF-ovi) za polinom proširene memorije (EMP) i polinom oslabljenje memorije (FMP) su programski podržani tako da se može napraviti ekspanzija do bilo kojeg stupnja. Kratko su razmotreni i promjena poretka i adaptacija dužine filtra. Dotaknute su i metode odbijanja jako raspršenih rezultata i Cramer-Raove konzistencije donje granice. VRF i njegovo opadanje za EMP filtar izvedeno je kao funkcija duljine (n) i izračunata je točka prijelaza gdje su VRF-ovi od EMP i FMP filtara jednaki. Predočeni su empirijski rezultati koji verificiraju izvod i implementaciju