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Signal Decomposition for Monitoring Systems of Processes


[ 1 ] Instytut Technologii Materiałów, Wydział Inżynierii Mechanicznej, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.9] Mechanical engineering

Year of publication


Published in


Journal year: 2024 | Journal volume: vol. 12 | Journal number: iss. 6

Article type

scientific article

Publication language


  • harmonic response
  • regulation
  • Fourier transform
  • Maclaurin series
  • process monitoring
  • automation

EN This article is devoted to the problem of signal decomposition into periodic and aperiodic components. According to the proposed approach, there is no need to evaluate the aperiodic component as a difference between the total signal of its periodic components. This research aims to create a general analytical approach that combines the Fourier and Maclaurin series methodologies into a single comprehensive series. As a result, analytical expressions for determining deposition coefficients were established for an aperiodic signal with a monoharmonic overlay. Recurrence relations were established to determine the coefficients of this series. These relations allow direct integrations of the obtained values of integrals to be avoided. The evaluated numerical values of the coefficients are also presented graphically and tabulated. It was proven that the values of these coefficients are universal numbers since they do not depend on the period/frequency of oscillations. The reliability of the proposed approach was confirmed by the fact that the evaluated coefficients are equal to the Fourier series coefficients in the case of a periodic signal. Also, for an aperiodic signal, these coefficients were reduced to the coefficients of the Maclaurin series. The usability of the proposed generalized analytical approach for signal decomposition is for control and monitoring systems of processes.

Date of online publication


Pages (from - to)

1188-1 - 1188-14





Article Number: 1188

License type

CC BY (attribution alone)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

at the time of publication

Ministry points / journal


Impact Factor

2,8 [List 2023]

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