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Nonstationary time series convolution: on the relation between the Hilbert–Huang and Fourier transform

AuthorsNeukirch, Maik ; García, Xavier
Hilbert-Huang transform
Fourier transform
Time series
Issue DateJan-2013
PublisherWorld Scientific Publishing
CitationAdvances in Adaptive Data Analysis 5(1) (2013)
AbstractThe Hilbert-Huang Transform (HHT) decomposes time series into intrinsic mode functions (IMF) in time-frequency domain. We show that time slices of IMFs equal time slices of Fourier series, where the instantaneous parameters of the IMF define the parameters amplitude and phase of the Fourier series. This leads to the formulation of the theorem that nonstationary convolution of an IMF with a general time domain response function translates into a multiplication of the IMF with the respective spectral domain response function which is explicitly permitted to vary over time. We conclude and show on a real world application that a de-trended signal's IMFs can be convolved independently and then be used for further time-frequency analysis. Finally, a discussion is opened on parallels in HHT and the Fourier transform with respect to the time-frequency domain
Description13 pages, 4 figures
Publisher version (URL)https://doi.org/10.1142/S1793536913500040
Identifiersdoi: 10.1142/S1793536913500040
issn: 1793-5369
e-issn: 1793-7175
Appears in Collections:(ICM) Artículos
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