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<p>We propose a scalar numerical differentiator in the form of a system of nonlinear differential equations of an arbitrary high order. We derive an explicit formula for the solution to this system and show that, under a suitable choice of the differentiator order, the error converges to zero for polynomial signals with additive white noise. For more general signals the error remains bounded. The feature of the proposed method is that it does not require any tuning parameters. We propose higher order cumulative smoothing algorithms for time series, which solve both interpolation and extrapolation problems without fitting any coefficients to the data. Bibliography: 7 titles.</p>

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MATHEMATICAL ASPECTS OF HIGHER ORDER UNIVERSAL NUMERICAL DIFFERENTIATOR FOR PARAMETER-FREE POLYNOMIAL ONLINE APPROXIMATION

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Igor Katrichek

摘要

We propose a scalar numerical differentiator in the form of a system of nonlinear differential equations of an arbitrary high order. We derive an explicit formula for the solution to this system and show that, under a suitable choice of the differentiator order, the error converges to zero for polynomial signals with additive white noise. For more general signals the error remains bounded. The feature of the proposed method is that it does not require any tuning parameters. We propose higher order cumulative smoothing algorithms for time series, which solve both interpolation and extrapolation problems without fitting any coefficients to the data. Bibliography: 7 titles.