Journal ArticleDOI
Design of variable and adaptive fractional order FIR differentiators
Reads0
Chats0
TLDR
The fractional differencing method and weighted least squares approach are presented and an adaptive fractional order differentiator is developed and applied to estimate the parameters of 1/f noise from the finite observation data set.About:
This article is published in Signal Processing.The article was published on 2006-10-01. It has received 102 citations till now. The article focuses on the topics: Fractional calculus & Adaptive algorithm.read more
Citations
More filters
Journal ArticleDOI
Studies on fractional order differentiators and integrators: A survey
TL;DR: Fractional order differentiators and integrators of order 12 and 14 are designed and implemented in real time using TMS320C6713 DSP processor and tested using National instruments education laboratory virtual instrumentation system (NIELVIS).
Journal ArticleDOI
Fractional Order Systems in Industrial Automation—A Survey
TL;DR: This paper describes linear and nonlinear cases with necessary stability and performance considerations for the benefit of a practicing engineer exploiting informatics in industry.
Journal ArticleDOI
Variable-order fractional derivatives and their numerical approximations
Duarte Valério,José Sá da Costa +1 more
TL;DR: This paper addresses the different possible definitions of variable-order derivatives and their numerical approximations; both approximation based upon the definitions and approximation consisting of non-linear transfer functions (in particular combining existing approximation of constant-order fractional derivatives, such as the Crone approximation, with fuzzy logic) are considered.
Journal ArticleDOI
A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
TL;DR: In this article, a survey of the recent relevant literature and findings in primary definitions, models, numerical methods and their applications is provided, which can help the readers for the selection of appropriate definition, model and numerical method to solve specific physical and engineering problems.
Journal ArticleDOI
Fractional spectral collocation methods for linear and nonlinear variable order FPDEs
TL;DR: An exponentially accurate fractional spectral collocation method for solving linear/nonlinear FPDEs with field-variable order and a spectral penalty method for enforcing inhomogeneous initial conditions are developed.
References
More filters
Book
Adaptive Filter Theory
TL;DR: In this paper, the authors propose a recursive least square adaptive filter (RLF) based on the Kalman filter, which is used as the unifying base for RLS Filters.
Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Journal ArticleDOI
Frequency-band complex noninteger differentiator: characterization and synthesis
TL;DR: In this article, the state-of-the-art on generalized (or any order) derivatives in physics and engineering sciences is outlined for justifying the interest of the noninteger differentiation.
Journal ArticleDOI
Splitting the unit delay [FIR/all pass filters design]
TL;DR: This work presents a comprehensive review of FIR and allpass filter design techniques for bandlimited approximation of a fractional digital delay, focusing on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value.