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Bootstrap Model Selection for Estimating the Sum of Exponentially Damped Sinusoids

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Innovations and Developments of Technologies in Medicine, Biology and Healthcare (EMBS ICS 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1360))

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Abstract

Model estimation is an important issue in signal processing since it enables to characterize the signal and to obtain some parameters providing information about its shape. An example of a model widely used in various fields of science is the sum of exponentially damped sinusoids. In this work, a new method for parameters estimation of such a model is proposed. This method uses nonlinear least squares together with Fourier transform to estimate parameters of the sum of damped sinusoids. For model order selection, a bootstrap method is utilized. First, the presented method is verified on simulated signals. The efficacy of model order selection is assessed for signals with a different set value of signal-to-noise (SNR) ratio. It is shown that for the models with orders from 2 to 7, the order was estimated correctly in all trials for SNR greater than 20 dB. If a proper model order is selected, the set values of signal parameters are included in the confidence intervals for parameters values, determined by the nonlinear least squares method. Afterward, the described method is used for modeling the event-related potential in magnetoencephalography (MEG) signal. The method gives good fitting results with \(\text {R}^{2}\) values greater than 0.9, showing its potential in MEG signals modeling and the assessment of brain activity.

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Acknowledgement

The author thanks D. Robert Iskander for his support and supervision at all stages of this work, and Cezary Sieluzycki for his help with MEG signals.

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Authors and Affiliations

  1. Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Marcela Niemczyk

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  1. Marcela Niemczyk
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Correspondence to Marcela Niemczyk .

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Editors and Affiliations

  1. Department of Biosensors and Processing of Biomedical Signals, Silesian University of Technology, Zabrze, Poland

    Natalia Piaseczna

  2. Department of Measurement and Electronics, AGH University of Technology, Kraków, Poland

    Magdalena Gorczowska

  3. Department of Biosensors and Processing of Biomedical Signals, Silesian University of Technology, Zabrze, Poland

    Agnieszka Łach

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Niemczyk, M. (2022). Bootstrap Model Selection for Estimating the Sum of Exponentially Damped Sinusoids. In: Piaseczna, N., Gorczowska, M., Łach, A. (eds) Innovations and Developments of Technologies in Medicine, Biology and Healthcare. EMBS ICS 2020. Advances in Intelligent Systems and Computing, vol 1360. Springer, Cham. https://doi.org/10.1007/978-3-030-88976-0_11

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