Time-Frequency Analysis for Non-Stationary Signal Diagnosis

Non-stationary signals, whose spectral content varies with time, arise in diverse domains such as machine vibration, biomedical monitoring and power-system stability. Traditional Fourier analysis, which assumes stationarity, is ill-suited to capture transient events or evolving oscillatory modes. Time-frequency analysis overcomes this limitation by mapping signal energy onto a two-dimensional plane of time and frequency. Core methods include the short-time Fourier transform (STFT), continuous wavelet transform (CWT) and their post-processing enhancements such as synchrosqueezing and reassignment. Those refinements sharpen the concentration of energy around instantaneous frequency trajectories, facilitating the extraction of weak components masked by noise or large-amplitude modes. Empirical mode decomposition (EMD) and its variants adaptively decompose signals into intrinsic mode functions, whose time-frequency signatures can then be more accurately tracked. Together, these tools enable robust diagnosis of faults in rotating machinery, detection of subsynchronous oscillations in power grids and characterisation of physiological rhythms. Recent algorithmic advances have focused on adaptive parameter selection, high-order transforms and optimised ridge extraction to improve resolution, suppress cross-term interference and enhance computational efficiency. The resulting methodologies support real-time monitoring, condition-based maintenance and early warning systems, underscoring the global significance of time-frequency analysis for non-stationary signal diagnosis.

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Time-Frequency Analysis for Non-Stationary Signal Diagnosis publication trend

The graph below shows the total number of articles in time-frequency analysis for non-stationary signal diagnosis across all publications each year (not limited to Nature Index journals).

Technical terms

Time-frequency representation (TFR): A depiction of signal energy or amplitude as a function of both time and frequency, revealing how spectral content evolves over time.

Short-time Fourier transform (STFT): A technique that applies the Fourier transform to successive, overlapping time windows to produce a time-frequency view of a signal.

Synchrosqueezing transform (SST): A post-processing method that reassigns and concentrates energy in a TFR around instantaneous frequency curves, enhancing readability.

Instantaneous frequency (IF): The local rate of phase change of a signal component, representing its time-varying frequency at each instant.

Empirical mode decomposition (EMD): An adaptive, data-driven method that decomposes a signal into intrinsic mode functions, each with well-behaved instantaneous frequencies.

References

1. Linear and synchrosqueezed time–frequency representations revisited: Overview, standards of use, resolution, reconstruction, concentration, and algorithms. Digital Signal Processing (2015).
2. Fault diagnosis of bearings in multiple working conditions based on adaptive time-varying parameters short-time Fourier synchronous squeeze transform. Measurement Science and Technology (2022).
3. Fractional Synchrosqueezing Transformation and its Application in the Estimation of the Instantaneous Frequency of a Rolling Bearing. IEEE Access (2020).
4. On Demodulation, Ridge Detection, and Synchrosqueezing for Multicomponent Signals. IEEE Transactions on Signal Processing (2017).
5. Application of Synchrosqueezed Wavelet Transforms for Extraction of the Oscillatory Parameters of Subsynchronous Oscillation in Power Systems. Energies (2018).
6. Modeling the Pulse Signal by Wave-Shape Function and Analyzing by Synchrosqueezing Transform. PLOS ONE (2016).