Signal Decomposition and Denoising Techniques in Non-Stationary Data
Summary
Non-stationary data abounds in fields as diverse as structural health monitoring, biomedical diagnostics and environmental sensing. Such signals often exhibit time-varying frequency content and amplitude, rendering classical Fourier-based filters inadequate. Contemporary research has therefore focused on adaptive decomposition methods that partition a complex signal into a set of simpler components, each reflecting a locally coherent oscillatory mode. Once separated, noise can be selectively suppressed by thresholding or reconstruction strategies. Empirical Mode Decomposition (EMD) and its variants—such as Ensemble EMD (EEMD) and Complete Ensemble EMD with Adaptive Noise (CEEMDAN)—decompose signals into Intrinsic Mode Functions (IMFs) without presuming stationarity. Variational Mode Decomposition (VMD) improves stability by framing mode extraction as an optimisation problem, seeking bandlimited modes via a constrained variational approach. Complementary techniques such as wavelet thresholding, singular spectrum analysis (SSA) and mutual information criteria are routinely combined with decomposition to enhance denoising performance. Recent advances integrate evolutionary or swarm-based algorithms to automate parameter tuning, ensuring robustness against heteroscedastic noise and preserving critical features. The resulting frameworks have been applied to fault diagnosis, remote sensing, seismic monitoring and acoustic measurement, underscoring their global importance and practical utility.
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Signal Decomposition and Denoising Techniques in Non-Stationary Data publication trend
The graph below shows the total number of articles in signal decomposition and denoising techniques in non-stationary data across all publications each year (not limited to Nature Index journals).
Technical terms
Intrinsic Mode Function (IMF): A component signal obtained by EMD or VMD, characterised by symmetric envelopes and a single extrema count per cycle, enabling meaningful instantaneous frequency estimation.
Empirical Mode Decomposition (EMD): An adaptive algorithm that iteratively extracts IMFs from a signal by sifting local extrema, without requiring predefined basis functions.
Variational Mode Decomposition (VMD): A constrained variational technique that decomposes a signal into bandlimited modes by minimising a composite cost function, often involving mode bandwidth and reconstruction fidelity.
Wavelet Thresholding: A denoising method that transforms signal components into the wavelet domain and applies hard or soft thresholds to suppress coefficients below a noise-dependent level.
Singular Spectrum Analysis (SSA): A nonparametric spectral estimation tool that decomposes a time series via singular value decomposition of its trajectory matrix, separating signal trends from noise.
References
- Bearing Fault Feature Extraction Method Based on GA‐VMD and Center Frequency. Mathematical Problems in Engineering (2022).
- An EEMD‐Based Denoising Method for Seismic Signal of High Arch Dam Combining Wavelet with Singular Spectrum Analysis. Shock and Vibration (2019).
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