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In this article, we propose the use of power function and least squares method for designing of a fractional order digital differentiator. The input signal is transformed into a power function by using Taylor series expansion, and its fractional derivative is computed using the Grunwald–Letnikov (G–L) definition. Next, the fractional order digital differentiator is modelled as a finite impulse response (FIR) system that yields fractional order derivative of the G–L type for a power function. The FIR system coefficients are obtained by using the least squares method. Two examples are used to demonstrate that the fractional derivative of the digital signals is computed by using the proposed technique. The results of the third and fourth examples reveal that the proposed technique gives superior performance in comparison with the existing techniques. [ABSTRACT FROM PUBLISHER]

Novel designs of third-order recursive wideband digital integrator and differentiator are presented. The integrator is obtained by interpolating two digital integration techniques, the Schneider-Kaneshige-Groutage (SKG) rule and the Trapezoidal rule. The differentiator is obtained by inverting the transfer function of the designed integrator after necessary modifications. The proposed integrator and differentiator approximate their ideal counterparts with absolute magnitude errors less than 0.02 and 0.14, respectively, over the entire frequency spectrum. Their performance compares favorably with existing integrators and differentiators. [ABSTRACT FROM AUTHOR]