Nonlinear Time-Frequency Analysis of Nonlinearly Coupled Electromagnetic Noise Sources

Ishiyama, Fumihiko; Maruyama, Masato

doi:10.1109/cspa55076.2022.9781968

Cited by 2 publications

(6 citation statements)

References 8 publications

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“…Note that major results are not affected by the parameters [7,14]. Conventional methods are easily affected by the parameters, because of the use of periodic boundary conditions.…”

Section: Discussionmentioning

confidence: 99%

“…Our method is based on a mode decomposition with general complex functions, which organize nonlinear oscillators [4][5][6][7][8], and we calculate the local linearized solution of the decomposition.…”

Section: Methodsmentioning

confidence: 99%

“…where f m (t) ∈ R represents the frequency modulation (FM) terms, which are known as "instantaneous frequency" by van der Pol [11], λ m (t) ∈ R represents the amplitude modulation (AM) terms, which correspond to our original [4][5][6][7] nonlinear trends, and c m (t 0 ) ∈ C represents the amplitudes of the oscillators at t = t 0 . This expansion corresponds to a mode decomposition with general complex functions, noting that…”

Section: Model Equationmentioning

confidence: 99%

“…and we can obtain unique H ′ m (t k ) easily by using the linear predictive coding (LPC) method with N samples, noting that we must use a non-standard numerical method to solve LPC [7,14].…”

Section: Local Linearized Solutionmentioning

confidence: 99%

“…We have a unique nonlinear method of time series analysis that provides an analytical perspective on numerically obtained nonlinear time series [4][5][6][7][8], and we apply the method to COVID-19 daily new cases in Japan to obtain analytical equation for nonlinear trends.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear trend of COVID-19 infection time series

Ishiyama

2023

NOLTA

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We have developed a nonlinear method of time series analysis that allows us to obtain multiple nonlinear trends without harmonics from a given set of numerical data. We propose to apply the method to recognize the ongoing status of COVID-19 infection with an analytical equation for nonlinear trends. We found that there is only a single nonlinear trend, and this result justifies the use of a week-based infection growth rate. In addition, the fit with the obtained analytical equation for the nonlinear trend holds for a duration of more than three months for the Delta variant infection time series. The fitting also visualizes the transition to the Omicron variant.

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“…Note that major results are not affected by the parameters [7,14]. Conventional methods are easily affected by the parameters, because of the use of periodic boundary conditions.…”

Section: Discussionmentioning

confidence: 99%