An alternative implementation of of fractional derivative/integral defined by Grunwald-Letnikov definition (GL) is introduced. By using the average of GL binomial coefficients along a window size instead of the real values of coefficients. Such an implementation can help in implementing large window-sized approximated GL with fewer resources which will help obtaining less error on a small amount of resources. For example, the proposed optimization can implement a GL integral of fractional order (? = -0.5) to sin(t) limited by a window size L of 1024 by the same resources that are used to implement a window size of 10 with an absolute error of 0.138 instead of 0.512. Another way to optimize resources usage of the fixed window method is by implementing different fractional-order operator for systems that do not require certain fractional-order such as PIDs. As different fractional-order requires a different amount of resources for the same output error. © 2021 IEEE.
Abdalrahman A., Soltan A., Radwan A.G.
Fractional Order; Grunwald-Letnikov derivative; Grunwald-Letnikov Integral
Midwest Symposium on Circuits and Systems, Vol. 2021-August, PP. 669 to 672, Doi: 10.1109/MWSCAS47672.2021.9531844