Time-Frequency Signal Processing and Analysis

Time-frequency signal processing is concerned with analysing how the spectral content of a signal evolves over time, offering a unified framework that bridges classical Fourier analysis with non-stationary signal characteristics. By mapping one-dimensional temporal data into a two-dimensional time-frequency plane, practitioners can reveal transient phenomena, frequency modulation and multi-component interactions that remain obscured in purely time- or frequency-domain approaches. Key methodologies range from the short-time Fourier transform, which applies sliding-window analysis to balance temporal and spectral resolution, to wavelet-based techniques that employ scale-dependent basis functions for adaptive localisation. Bilinear distributions such as the Wigner–Ville distribution achieve high resolution by considering signal auto-correlations, albeit at the cost of cross-term artefacts, which have been mitigated by kernel design and hybrid masking strategies. Mode decomposition methods, including variational mode decomposition and empirical wavelet transform, adapt to signal structure by extracting intrinsic oscillatory components, facilitating precise isolation of signal modes. Advances in machine learning have been harnessed to refine denoising, component separation and feature extraction, underpinning applications from structural health monitoring and machinery fault diagnosis to biomedical spectroscopy and communications. Contemporary research continues to enhance resolution limits, suppress interference and improve computational efficiency, driving time-frequency analysis towards real-time and large-scale data challenges with global significance across diverse scientific and engineering domains.

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Time-Frequency Signal Processing and Analysis publication trend

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

Technical terms

Short-time Fourier transform (STFT): A technique that computes the Fourier transform within successive time windows to analyse how signal frequency content changes over time.

Wavelet transform (WT): A method using scalable, localised oscillatory functions to represent signals at multiple resolutions in time and frequency.

Wigner–Ville distribution (WVD): A bilinear time-frequency representation offering high resolution by correlating a signal with shifted versions of itself but prone to cross-term interference.

Variational mode decomposition (VMD): An algorithm that decomposes a signal into a set of band-limited intrinsic mode functions by solving an optimisation problem.

Empirical wavelet transform (EWT): A data-driven approach that partitions the Fourier spectrum into adaptive bands and constructs wavelet filters to extract signal components.

S-transform: A hybrid analysis tool combining elements of the STFT and wavelet transform to provide frequency-dependent resolution with phase information.

References

1. Novel Fourier quadrature transforms and analytic signal representations for nonlinear and non-stationary time-series analysis. Royal Society Open Science (2018).
2. Denoising of Raman Spectra Using a Neural Network Based on Variational Mode Decomposition, Empirical Wavelet Transform, and Encoder-Bidirectional Long Short-Term Memory. Applied Sciences (2023).
3. Investigation and evaluation of cross-term reduction in masked Wigner-Ville distributions using S-transforms. PLOS ONE (2024).