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arXiv · 2504.08453

Successive Jump and Mode Decomposition

Mojtaba Nazari·Anders Rosendal Korshøj·Naveed ur Rehman
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Abstract

We propose fully data-driven variational methods, termed successive jump and mode decomposition (SJMD) and its multivariate extension, successive multivariate jump and mode decomposition (SMJMD), for successively decomposing nonstationary signals into amplitude- and frequency-modulated (AM-FM) oscillations and jump components. Unlike existing methods that treat oscillatory modes and jump discontinuities separately and often require prior knowledge of the number of components (K) -- which is difficult to obtain in practice -- our approaches employ successive optimization-based schemes that jointly handle AM-FM oscillations and jump discontinuities without the need to predefine K. Empirical evaluations on synthetic and real-world datasets demonstrate that the proposed algorithms offer superior accuracy and computational efficiency compared to state-of-the-art methods.

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Mojtaba Nazari, Anders Rosendal Korshøj, Naveed ur Rehman. 2025-04-11. Successive Jump and Mode Decomposition. https://arxiv.org/abs/2504.08453

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