Fractional order differentiation by integration and error analysis in noisy environment: Part 2 discrete case
type: Dataset
description: In the first part of this work, the differentiation by integration method has been generalized from the integer order to the fractional order so as to estimate the fractional order derivatives of noisy signals. The estimation errors for the proposed fractional order Jacobi differentiators have been studied in continuous case. In this paper, the focus is on the study of these differentiators in discrete case. Firstly, the noise error contribution due to a large class of stochastic processes is studied in discrete case. In particular, it is shown that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, the mean value and variance functions of which are time-variant. Secondly, by using the obtained noise error bound and the error bound for the bias term error obtained in the first part, we analyze the design parameters' influence on the obtained fractional order differentiators. Thirdly, according to the knowledge of the design parameters' influence, the fractional order Jacobi differentiators are significantly improved by admitting a time-delay. In order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, numerical simulations show their accuracy and robustness with respect to corrupting noises.
issued: 2026-05-15T00:56:35.432365
language: en
modified: 2026-05-15T00:56:35.432370
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticspreprint
keyword: infoinfo-tscomputer-science-cssignal-and-image-processing
keyword: mathmath-namathematics-mathnumerical-analysis-mathna
keyword: preprints-working-papers-
keyword: spisignalengineering-sciences-physicssignal-and-image-processing
landing page: https://inria.hal.science/hal-00779182

Fractional order differentiation by integration and error analysis in noisy environment: Part 2 discrete case
type: Distribution
format: HTML
issued: 2026-05-15T00:56:35.445066
modified: 2026-05-15T00:56:35.420339
access URL: https://inria.hal.science/hal-00779182

test_moissonnage_selune
type: Agent