[en] Various numerical differentiation methods have been developed to compute an approximated derivative of the signal from its discrete values. Amongst them, one of the most commonly applied is the finite difference method.
Particularly in the case of experimental data, substantial noise or imprecision may be present in the signal. And here is the crux of the matter: straightforward schemes with short-differentiation steps will amplify this noise, often so much that the result appears to be unusable. While increasing the differentiation step has the positive effect of decreasing the noise, it also has two adverse effects: it produces a time shift compared with what would have been expected, and it introduces distortion by broadening and flattening the narrow features.
The present study will focus on the moving-average filter on one hand, and on differentiation by some usual finite difference schemes on the other hand. Amongst relevant parameters, the influence of the sampling period and the differentiation step will be examined, in particular regarding their consequence on the time-accuracy and the noise filtering effect of the considered methods.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Dumont, Fabien ; Université de Liège - ULiège > Département ArGEnCo > Ingénierie du feu
Language :
English
Title :
Analysis of some finite difference schemes for slightly noisy time dependent signals
Alternative titles :
[fr] Analyse de quelques schémas aux différences finies pour signaux temporels légèrement bruités
