Signal Processing

Signal processing is the discipline that transforms, analyses and synthesises information-bearing signals to extract useful features, to suppress unwanted components, or to prepare data for decision-making. Signals may be continuous or discrete, deterministic or stochastic, and span domains as diverse as time, frequency and space. Core operations include linear and nonlinear filtering, time–frequency decompositions, convolution and correlation, and statistical estimation. Classical methods rely on transforms such as the Fourier, Laplace and Z-transforms, which recast differential or difference equations into algebraic form. Modern developments extend these foundations: wavelet and synchrosqueezing techniques adaptively decompose non-stationary signals; sparse and tensor approaches reveal multidimensional structure; and adaptive algorithms track time-varying environments by minimising error criteria in real time. Overarching trends marry signal processing with machine learning, enabling data-driven models for classification, detection and prediction across fields from communications and radar to biomedical monitoring and audio analysis.

Research from Nature Portfolio

A comprehensive comparative study has evaluated leading non-stationary signal decomposition algorithms in both single- and multichannel settings. Empirical mode decomposition, variational mode decomposition, synchrosqueezed transforms and sliding singular spectrum analysis were tested on synthetic benchmarks and real-world measurements, with attention to mode-alignment, noise robustness and parameter sensitivity. The work provides practical guidelines for selecting and tuning methods to extract adaptive amplitude- and frequency-modulated components for fault diagnosis, biomedical monitoring or environmental sensing. In another contribution, a novel spectrum-feature extraction framework has combined Allan variance, variational mode decomposition and power-spectral density techniques to identify reliable vibration frequencies in micro-seismic recordings. By filtering multiaxis accelerometer data, isolating resonant modes and applying Allan variance to rank modal stability, the method accurately recovered seismic excitation frequencies, demonstrating potential for structural health monitoring of heritage monuments under extreme environmental conditions.

Research from all publishers

A survey of underwater acoustic communications has mapped advances in physical-layer design, comparing cyclic-prefix OFDM, filter-bank multicarrier methods, MIMO architectures and emerging index-modulation schemes. The review addresses severe multipath, Doppler spread and ambient noise in shallow and deep water, and highlights joint adaptive equalisation and Doppler compensation strategies that enable reliable links for autonomous underwater vehicles and sensor networks. In the wireless-security domain, a deep-learning recovery scheme for frequency-hopping sequences integrates time–frequency analysis with a convolutional neural network and gated recurrent units. By combining residual-network feature extraction and sequence modelling, the method estimates hopping patterns with high generalisation across diverse channel conditions, achieving near-ideal bit-error-rate performance and enabling robust anti-jamming receivers in dynamic electromagnetic environments.

Signal Processing publication trend

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

Technical terms

Convolution: A linear operation combining two sequences to produce a third, representing the response of an LTI system to an input.

Time–frequency decomposition: Techniques such as short-time Fourier or wavelet transforms that represent a signal’s spectral content as it evolves over time.

Adaptive filter: A filter whose coefficients update in real time (e.g. via least-mean-squares) to track changing signal or noise statistics.

Empirical Mode Decomposition (EMD): A data-driven method that iteratively extracts intrinsic mode functions by identifying local extrema and constructing envelope means.

Variational Mode Decomposition (VMD): An optimisation-based decomposition that extracts band-limited modes by minimising a predefined constrained cost in the spectral domain.

Allan variance: A measure of frequency stability used to assess noise processes and to identify reliable signal components over different averaging times.

Mode alignment: The enforcement of consistent decomposition across multiple channels so that corresponding modes can be directly compared and fused.

References

1. Data-driven nonstationary signal decomposition approaches: a comparative analysis. Scientific Reports (2023).
2. Spectrum feature extraction method combining Allan variance, VMD, and PSD. Scientific Reports (2024).
3. A Survey on Physical Layer Techniques and Challenges in Underwater Communication Systems. Journal of Marine Science and Engineering (2023).
4. Deep-Learning-Based Recovery of Frequency-Hopping Sequences for Anti-Jamming Applications. Electronics (2023).