Aims. The revised dataset of sunspot and group numbers (released by WDC-SILSO) and the sunspot number reconstruction based on dendrochronologically dated radiocarbon concentrations have been analyzed to provide a deeper characterization of the solar activity main periodicities and to investigate the role of the Gleissberg and Suess cycles in the grand minima occurrence. Methods. Empirical mode decomposition (EMD) has been used to isolate the time behavior of the different solar activity periodicities. A general consistency among the results from all the analyzed datasets verifies the reliability of the EMD approach. Results. The analysis on the revised sunspot data indicates that the highest energy content is associated with the Schwabe cycle. In correspondence with the grand minima (Maunder and Dalton), the frequency of this cycle changes to longer timescales of ~14 yr. The Gleissberg and Suess cycles, with timescales of 60?120 yr and ~ 200?300 yr, respectively, represent the most energetic contribution to sunspot number reconstruction records and are both found to be characterized by multiple scales of oscillation. The grand minima generation and the origin of the two expected distinct types of grand minima, Maunder and longer Sp?rer-like, are naturally explained through the EMD approach. We found that the grand minima sequence is produced by the coupling between Gleissberg and Suess cycles, the latter being responsible for the most intense and longest Sp?rer-like minima (with typical duration longer than 80 yr). Finally, we identified a non-solar component, characterized by a very long scale oscillation of ~?7000 yr, and the Hallstatt cycle ( ~?2000 yr), likely due to the solar activity. Conclusions. These results provide new observational constraints on the properties of the solar cycle periodicities, the grand minima generation, and thus the long-term behavior of the solar dynamo.
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