Complex Systems and Signal Processing Research Group

The Complex Systems and Signal Processing research group is internationally leading in the development of techniques and algorithms for complex systems analysis, control and signal processing and the application of these in emerging areas of science, engineering and medicine.

View of Sheffield city centre at dusk

The group is renowned for its work on the identification and analysis of complex spatio-temporal systems, nonlinear signal processing, and the analysis and design of nonlinear systems in the frequency domain.

Research themes

Our research provides the underpinning signal processing, system identification, dynamical analysis, control and modelling to support emerging multi-disciplinary research themes.

Nonlinear System Identification and Information Processing

The group has pioneered the most advanced nonlinear system identification and information processing methodology, tools and algorithms available to date, which can be applied to a wide class of nonlinear complex dynamical systems, including chaotic, spatio-temporal and stochastic systems.

A wide class of nonlinear models is being investigated, including polynomial, radial basis function and wavelet multiresolution models.

The focus of research is on model structure selection and the identification of models that a) capture the underlying dynamics rather than fit the data and b) provide insight into or predict fundamental properties of the system of interest.

The derivation of generic model validity test and model analysis methods for all classes of nonlinear models are also being studied.

The methods and tools developed by the group have been successfully used to develop the Sheffield online GEO forecast tool, providing the most accurate two-day-ahead forecast available of the electron flux.

Forecasting the evolution of these fluxes enables mitigation of their effects on spacecraft.

The group is also carrying out research to reverse-engineer neural processes using a wide range of experimental data sets, including electrophysiological, EEG, MRI and DOT recordings.

In collaboration with researchers in other disciplines we model the visual system of the fruit flies to understand how fly brains process information about the visual environment. In collaboration with NHS clinicians we developed causality detection and wavelet adaptive tracking algorithms to predict the onset of epileptic seizures.

Further Information:
Sheffield online GEO forecast tool

Frequency Domain Analysis of Nonlinear Systems

The group has developed a complete theory for the analysis of nonlinear systems in the frequency domain. This consists of analytic methods for mapping from nonlinear discrete and continuous time nonlinear differential equation models to the multi-dimensional generalised frequency response functions and vice versa.

A new class of filters, called energy transfer filters, has recently been derived which allows energy to be moved to new frequency locations or spread over a band of frequencies.

The focus of current research is to extend the theory, methods and algorithms, developed for analysing and synthesising lumped nonlinear systems in the frequency domain, to spatio-temporal systems.

The higher-order frequency response analysis tool developed by the group has been successfully used to elucidate for the first time, as part of a BBSRC funded project, the nonlinear coding mechanisms implemented by fly photoreceptors to encode and enhance salient stimuli features that are behaviourally important.

Further Information:
Reverse Engineering Drosophila Retinal Networks

Complex, Spatio-Temporal Systems

Many biological, chemical and physical systems involve variables which depend on both space and time. Such systems, which often operate away from equilibrium, exhibit complex emergent behaviour such as pattern formation, self organization, turbulence, spatio-temporal chaos etc.

The goal of this research is to use this data and extract informative structures, reconstruct the underlying spatio-temporal dynamics that govern these systems as well as analyse, understand and forecast their emerging properties.

The realisation, identification, prediction, analysis and control of this class of systems are being studied at theoretical level, with the aim to develop practical methodologies and tools that can help address big research challenges in energy, environment, life sciences etc.

The tools developed as part of this research have been applied successfully to study iceberg calving patterns and climate change in Greenland, model and control of crystal growth, fluid flows and wildfires.

The group is also carrying out research on the multiscale modelling of musculoskeletal system in biomedical system engineering and the differentially expressed gene modelling in biology.


The Complex Systems and Signal Processing research group has an applied engineering focus involving multi-disciplinary collaboration via engineering companies and industrial research institutes. Here are some examples of collaborative partnerships.


The group has successfully developed individual blade-pitch control algorithms to attenuate the harmful structural loads experienced by wind turbine generators.

This control solution is currently being benchmarked by Vestas in-house, to establish the business case for taking the design forward to production.

Building on the group’s success in estimating complex fluid flows, wind turbine gust prediction techniques have been pioneered using measurements from state-of-the-art Light Detection and Ranging (LiDAR) instruments. This project was supported by Vestas and has yielded a system that can pinpoint the strength, direction and location of oncoming gusts of wind.

This paves the way for designing preview blade-pitch control systems that will dramatically reduce harmful wind turbine loads.

Bae Systems

It is well known that increasing damping can improve vibration performance around resonance but is often detrimental for performance at higher frequencies. The group has rigorously proven that nonlinear damping can systematically resolve this fundamental problem.

The result provides the foundation for solutions to a wide range of challenging vibration control problems and has enabled the development of new magneto-rheological damper based smart actuators, and novel damping for a BAE Systems rig.

The outcomes have also initiated significant application studies involving vibration control of an offshore wind tower in Germany.

Sheffield Teaching Hospitals

In collaboration with NHS neurologists, the group has developed the first reliable method to detect the onset of epileptic seizure several seconds before the seizure occurs.

An electroencephalogram (EEG) is routinely used in the evaluation of brain disorders including the diagnosis and treatment of epilepsy.

The group has introduced fundamentally new algorithms to model time varying processes, to track rapid parameter variations, and map these to frequency domain behaviours.

The algorithms have now been incorporated into existing EEG software packages and following full ethical approval has been used in clinical practice at the Sheffield Hallam Teaching Hospital NHS Foundation Trust.


We are a multidisciplinary team, carrying out world-class research and widely recognised for our outstanding achievements and contributions to the international research community.

Core members


Research centres

We have sought to extend our research user base laterally by participating in research centres. Group leader Professor Billings also heads the Centre for Signal Processing and Complex Systems (CSPCS) and the group is also actively involved in the Solar Physics and Space Plasma Research Centre (SP2RC).

Centre for Signal Processing and Complex Systems

Multi-disciplinary research

The Centre for Signal Processing and Complex Systems supports a diverse range of multi-disciplinary research projects that span several departments and institutions.

The centre provides the underpinning signal processing, system identification, dynamical analysis, control and modelling to support emerging multi-disciplinary research themes in medicine, systems and synthetic biology, stem cell dynamics, neuro-imaging, bio-imaging, neural processing in Drosophila, reaction-diffusion systems, non-equilibrium growth processes, studies of solar terrestrial systems, mobile robots, volatility modelling and financial systems, climate dynamics, nonlinear materials design and many other complex phenomena.

Research aims

The aims of the centre are twofold: First, to elaborate developments of nonlinear signal and information processing methods from a generic systems engineering perspective. Secondly, to extend and develop the systems engineering algorithms to address the specific problems associated with each of the multi-disciplinary topics above.

We expect this research to naturally evolve to include other cross-disciplinary research themes and to stimulate further collaboration between disciplines, departments and institutions.

Most of the research is funded from the research councils and similar bodies with grant capture by the founding members over the last three years of over £25m.

Solar Physics and Space Plasma Research Centre

The Centre is at the forefront of addressing theoretical and observational issues in solar and solar system physics that include solar magneto-seismology, dynamics of the solar atmosphere, solar wind, magnetosphere and Space Weather.

More centre information

Space Systems Laboratory

Our Space Systems Laboratory (SSL) conducts world class research in the field of experimental and theoretical space plasma and solar physics. Our aim is to investigate the physical processes in the solar atmosphere and the effect this has on our local geospace environment.

We are also involved in the design, manufacture, and operation of satellite borne instrumentation and have a long history of involvement in high profile space missions.

SSL’s collaboration with the Complex Systems and Signal Processing Research group has enabled members of SSL to apply data analysis and modelling methods developed within the field of Systems Engineering to problems within the field of Space Plasma Physics.

We have also established a new High Performance Computing Lab equipped with £150k FPGA, GPU and SpiNNaker hardware.

More laboratory information

Research team

Our impact culture encourages all staff to seek out collaborations independently and to respond flexibly to emerging opportunities. An example of impact from this research group is Professor Balikhin’s work with ESA and NASA that led to the development of algorithms to clean magnetic field observations from the Venus Express spacecraft that were previously unusable owing to the lack of shielding.

Centres of excellence

The University's cross-faculty research centres harness our interdisciplinary expertise to solve the world's most pressing challenges.