Adaptive Multi-Resolution Dynamic Mode Decomposition for Non-Stationary Signal Analysis

Non-stationary signals with rapidly evolving and overlapping spectral components present challenges for obtaining accurate time-frequency distribution (TFD). Conventional dynamic mode decomposition (DMD) extracts mode frequencies and damping information but struggles to represent the TFD of highly non-stationary signals. Multi-resolution DMD (MR-DMD) improves this but depends on a fixed embedding dimension, causing mode mixing and reduced resolution. This paper presents an adaptive multiresolution DMD (AMR-DMD) technique that automatically determines the embedding dimension at each decomposition level using a time-frequency resolution criterion obtained from the Heisenberg uncertainty principle for real-valued signals. The method is further extended to complex-valued signals by separating positive and negative frequency components for complete spectral characterization. Hilbert spectral analysis (HSA) is applied to the modes obtained from AMR-DMD to generate the TFD. Experimental results on real synthetic and complex signals show that the proposed AMR-DMD-based HSA technique provides improved TFDs, achieving sharper localization, lower reconstruction error, and higher quality reconstruction factor compared with empirical mode decomposition-based HSA, variational mode decomposition-based HSA, DMD-based HSA, and MR-DMD-based HSA methods.