New design of full band differentiators based on Taylor series

Abstract

The classical central difference approximations of the derivative of a function based on Taylor series are the same as type III maximally linear digital differentiators for low frequencies. A new ®nite difference formula is derived, which can be implemented as a fullband type IV maximally linear differentiator. The differentiator is compared with type III maximally linear and type IV equiripple minimax differentiators. A modi®cation is proposed in the design to minimise the region of inaccuracy near the Nyquist frequency edge.

On algebraic time-derivative estimation and deadbeat state reconstruction

“…Finally, and although it is clearly beyond the scope of the present paper, note that because of the convolution form of algebraic estimation (2), the latter can also be connected with Finite-Impulse Response (FIR) differentiators, on which numerous studies and results were published (see [17], [31] and references therein), with the minor difference that these differentiators are usually described in a discrete-time framework, although it is clear that a comparison similar to the present paper could also be carried out in discrete-time.…”

Fractional Euler analog-to-digital transform

“…Although these methods are simple and easy to use to fit the ideal differentiator, they have large magnitude distortion in the high-frequency range. To enhance the fitting of the ideal differentiator in high-frequencies, several design techniques have been proposed such as Al-Alaoui transform [2], Taylor series method [3], the quadratic programming method [4], wideband differentiator [5], differentiator using fractional delay filter [6,7] and fractional bilinear transform [8]. More recently, wideband recursive digital differentiators with relatively lower errors have been proposed in Upadhyay [9] and Al-Aloui [10].…”

Design of Improved Fractional Order Integrators using Indirect Discretization Method

“…Since 1960s [16][17][18][19][20], different well established mathematical concepts have been explored for the formulation of RC networks for realizations of capacitors, RC impedances and RC admittances for non-integer orders. Various Taylor series based methods [21][22] also helped in finding the solutions of fractional order (f-o) systems for realizing them in their physical forms with finite memory. Researchers started taking interest for designing rational approximations for fractional order differentiators (FODs) and fractional order integrators (FOIs) in the beginning of last decade and gave many techniques namely Prony's method [23], Ostaloup approximation [24] and Laguerre approximation [25], but still there is much scope of doing work in design of different suitable approximation techniques.…”