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

AutorNeukirch, Mail ; García, Xavier
Palabras claveNonstationary
Hilbert-Huang transform
Fourier transform
Time series
Fecha de publicaciónene-2013
EditorWorld Scientific Publishing
CitaciónAdvances in Adaptive Data Analysis 5(1) (2013)
ResumenThe 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
Descripción13 pages, 4 figures
Versión del editorhttp://dx.doi.org/10.1142/S1793536913500040
Identificadoresdoi: 10.1142/S1793536913500040
issn: 1793-5369
e-issn: 1793-7175
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