An arbitrary-order differentiator design paradigm with adaptive gains

Robust exact uniformly convergent arbitrary order differentiator

An arbitrary order differentiator that, in the absence of noise, converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented. The only assumption on a signal to be differentiated (n−1)-times is that its n-th derivative is uniformly bounded by a known constant. The proposed differentiator switches from a newly designed uniform ...

Arbitrary-order all-fiber temporal differentiator based on a fiber Bragg grating: design and experimental demonstration.

A new technique to design an all-fiber temporal differentiator that has a large bandwidth and an arbitrary differentiation order is proposed and investigated. The proposed temporal differentiator is a special fiber Bragg grating (FBG) that is designed by controlling its magnitude and phase responses with the discrete layer peeling (DLP) method. There are three important features of this techniq...

Analysis and Design of Fractional Order Digital Differentiator

Design of Fractional Order Differentiator Using Feedback System

A new feedback-based methodology for the implementation of a fractional-order differentiator (FD) is described in this paper. The differentiator can be based on a standard definition of the fractional calculus, such as the Riemann-Liouville or Grunwald-Letnikov definitions. Some methods by which the FD functions can be approximated using a DSP-based implementation (either FIR or IIR) are descri...

On distributed order integrator/differentiator

In this paper, we derive the impulse response of the distributed order integrator/ differentiator and its asymptotic property by using the complex path integral. Based on the derived analytical impulse response, we present a technique to perform the discretization of the above distributed order integrator/differentiator. The derived asymptotic property can be applied to verify the feasibility o...