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In this paper, a simple approach is proposed to design recursive digital differentiators and integrators by applying the concept of time-constant analysis. The time-constant combined with the magnitude response describes the system behavior of a digital differentiator and an integrator. Further, new recursive digital differentiator and integrator designs of first-order systems are also obtained for more accurate or comparable magnitude responses as compared to the existing designs of higher-order systems over wideband. These designs are more suitable for control systems and signal processing applications.

A Simple Approach to Design Recursive Digital Differentiators and Integrators