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Uniformly Damped Binomial Filters: Five-percent Maximum Overshoot Optimal Response Design

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Abstract

In this paper, the five-percent maximum overshoot design of uniformly damped binomial filters (transfer functions) is introduced. First, the Butterworth filter response is represented as a damped binomial filter response. To extend the maximum overshoot response of the second-order Butterworth to higher orders, the binomial theorem is extended to the uniformly damped binomial theorem. It is shown that the five-percent uniformly damped binomial filter is a compromise between the Butterworth filter and the standard binomial filter, with respect to the filter approximation problem in the time and frequency domain. Finally, this paper concludes that in applications of interest, such as step-tracking, where both strong filtering and a fast, smooth transient response with negligible overshoot are desired, the response of the normalized five-percent uniformly damped binomial form is a candidate replacement for both the Butterworth and standard binomial filter forms.

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Author notes

  1. Kayode Akingbade and Folasade Dahunsi have contributed equally to this work.

Authors and Affiliations

  1. Department of Computer Engineering, Federal University of Technology Akure, PMB 704, Akure, Ondo, Nigeria

    Oluwasegun Somefun & Folasade Dahunsi

  2. Department of Electrical and Electronics Engineering, Federal University of Technology Akure, PMB 704, Akure, Ondo, Nigeria

    Kayode Akingbade

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  1. Oluwasegun Somefun
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Correspondence to Oluwasegun Somefun.

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The code used to develop this article can be found on Github https://github.com/somefunagba/sff.

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Somefun, O., Akingbade, K. & Dahunsi, F. Uniformly Damped Binomial Filters: Five-percent Maximum Overshoot Optimal Response Design. Circuits Syst Signal Process 41, 3282–3305 (2022). https://doi.org/10.1007/s00034-021-01931-2

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