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
uobicˇajeno se rade za ravnomjerno raspored¯ene tocˇke u prostoru. U ovom radu dana je derivacija polinomnih filtara
za neravnomjerno raspored¯ene tocˇke. 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 izraˇcunata je toˇcka prijelaza gdje su VRF-ovi od EMP i FMP
filtara jednaki. Predoˇceni su empirijski rezultati koji verificiraju izvod i implementaciju.
