On the Efficient Implementation of an Implicit Discrete-Time Differentiator

TL;DR

This paper introduces optimized algorithms for implicit discrete-time differentiators, utilizing Horner's and Shaw-Traub methods to significantly reduce implementation time and computational complexity.

Contribution

It presents novel implementation techniques that improve efficiency of discrete-time differentiators by applying specific polynomial evaluation algorithms.

Findings

Half-Horner and Full-Horner methods outperform others in speed and efficiency

Algorithms are effective for differentiators of orders 3, 7, and 10

Significant reduction in simulation time achieved

Abstract

New methodologies are designed to reduce the time complexity of an implicit discrete-time differentiator and the simulation time to implement it. They rely on Horner's method and the Shaw-Traub algorithm. The algorithms are compared for differentiators of orders 3, 7, and 10. The Half-Horner and Full-Horner methods showed the best performance and time complexity.