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Analysis of the intrinsic mode functions. (English) Zbl 1100.94006
Summary: The Empirical Mode Decomposition is a process for signals which produces Intrinsic Mode Functions from which instantaneous frequencies may be extracted by simple application of the Hilbert transform. The beauty of this method to generate redundant representations is in its simplicity and its effectiveness.
Our study has two objectives: first, to provide an alternate characterization of the Intrinsic Mode components into which the signal is decomposed and, second, to better understand the resulting polar representations, specifically the ones which are produced by the Hilbert transform of these intrinsic modes.

MSC:
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
44A15 Special integral transforms (Legendre, Hilbert, etc.)
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
34B24 Sturm-Liouville theory
93B30 System identification
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