Cubic polynomial and cubic rational <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e960" altimg="si4.gif"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math> sign, monotonicity and convexity preserving Hermite interpolation

Gabrielides, Nikolaos C.; Sapidis, Nickolas S.

doi:10.1016/j.cam.2019.02.024

Cited by 6 publications

(1 citation statement)

References 34 publications

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“…However, the standard cubic Hermite interpolation has two shortcomings when the different conditions are given: (1) the smoothness of the interpolated curve is lacking. (2) The interpolated shape cannot be changed and cannot be adjusted flexibly according to the actual situation (Gabrielides and Sapidis 2019).…”

Section: Introductionmentioning

confidence: 99%

A three-dimensional adaptive rational interpolation algorithm for removing TMS-EEG pulse artifacts

Xiong,

Di,

Liu

et al. 2023

Physiol. Meas.

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Objective. Transcranial magnetic stimulation in combination with electroencephalography (TMS-EEG) has been widely used to study the reactivity and connectivity of brain regions. In order to efficiently and fast solve the pulse artifacts problem caused by TMS electromagnetic pulses, a three-dimensional adaptive rational quadratic Hermite interpolation algorithm is proposed. Approach. Firstly, a three-dimensional signal matrix is obtained by a signal recombination algorithm, where the removed window is automatically obtained by a derivative threshold. Secondly, the adaptive rational quartic Hermite interpolation algorithm is used to interpolate the removed window. Finally, the performance of the algorithm is verified using simulated and public database data. Main results. The simulation results show that the proposed algorithm improves the SNR by 23.88%~47.60%, reduces the RMSE by 46.52%~81.11%, reduces the average MAE by 47.83%~58.33%, and reduces the time consumption of the proposed algorithm by 45.90% compared with the piecewise cubic Hermite interpolation algorithm. Significance. Therefore, TMS-EEG pulse artifacts can be removed effectively and quickly with the proposed algorithm.

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Section: Introductionmentioning

confidence: 99%