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Given a dataset of a signal which has been decomposed into its IMfs (with EMD (Hilbert-Huang transform)), how can synthetic replicas of that signal be reproduced from the decomposed signal? There are various signal components that need to be taken into account such as the stitching to account for the continuity and the 'edges'. This can be seen in Fig5. of online EMD methodology where the later IMFs do not span the full time like of the data and are 'irregular'.

Are there frameworks for these productions or suitable heuristics would suffice? Can each IMF be sampled according to assumptions such as them being iid? GMMs appear to be used for detection but it seems not suitable for the temporal dependencies, GMMs for signal detection

Would the choice of the windowing used for the processing of the signal have any effect on how the signals should be reproduced? If the decomposition is done on truncated block forms of the signal, can trails be used as components of their own contribution (treated as a residual member).

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