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Closed Form Approach for Constrained Design of nth-Order IIR Digital Differentiator

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Abstract

This work presents a new design method for nth-order infinite impulse response (IIR) differentiators. First, the cost function of the IIR differentiator is derived in closed form without frequency sampling. Next, a new optimization scheme is proposed to minimize the cost function under the pole radius constraint. Here, the magnitude and phase specifications are approximated simultaneously with a stability margin. Furthermore, discrete optimization for the IIR differentiator is presented for a specified word length constraint. The discrete optimization results in a stable IIR differentiator with finite word length coefficients owing to the stability margin. Finally, several design examples are demonstrated to evaluate the efficiency of the proposed method.

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Acknowledgements

The authors would like to express sincere thanks to the anonymous reviewers for their valuable comments. This work was supported in part by the research grant from the Mazda Foundation.

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Authors and Affiliations

  1. Graduate School of Advanced Science and Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi-Hiroshima, Hiroshima, 7398527, Japan

    Masayoshi Nakamoto

  2. Department of Applied Electronics, Tokyo University of Science, 6-3-1, Niijuku, Katsushika-ku, Tokyo, 1258585, Japan

    Naoyuki Aikawa

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  1. Masayoshi Nakamoto
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  2. Naoyuki Aikawa
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Correspondence to Masayoshi Nakamoto.

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Nakamoto, M., Aikawa, N. Closed Form Approach for Constrained Design of nth-Order IIR Digital Differentiator. Circuits Syst Signal Process 42, 3385–3411 (2023). https://doi.org/10.1007/s00034-022-02264-4

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