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Unified Sparse Time–Frequency Analysis: Decomposition, Transformation, and Reassignment

Time–frequency (TF) analysis is essential for industrial engineering applications. However, the conventional TF analysis methods suffer from blurry TF energy. This article proposes a new unified sparse TA analysis (STFA) framework to concentrate the blurry energy, restrain noise, separate condition-related components, and retain the signal reconstruction property. The STFA framework leverages the weighted elastic net sparse regularization for sparsity- inducing and energy concentration and uses the reconstruction error term for condition-related component separation and signal reconstruction, which bridges the gaps among sparsity, decomposition, transformation, and reassignment. Theoretical analysis and comprehensive investigation of the proposed framework are performed in practical cases. Comparison results with the state-of-the-art methods demonstrate that the proposed framework has superior properties for TF feature energy concentration, denoising, component separation, and reconstruction, especially for the signals with the fast-varying features.