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Spectral analysis for nonstationary and nonlinear systems: a discrete-time-model-based approach
Fei He1, Stephen A Billings, Hua-Liang Wei
1Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD, UK. f.he@sheffield.ac.uk
IEEE Transactions on Bio-Medical Engineering
|March 20, 2013
Summary
This study introduces a new frequency-domain analysis for nonlinear time-varying systems using parametric models. It enables tracking nonlinear frequency features like intermodulation and energy transfer in complex data.
Area of Science:
- Signal Processing
- Nonlinear Dynamics
- Biomedical Engineering
Background:
- Analyzing nonlinear time-varying systems is challenging.
- Existing methods struggle to capture dynamic frequency features.
- Understanding such systems is crucial in fields like neuroscience.
Purpose of the Study:
- Introduce a novel frequency-domain analysis framework for nonlinear time-varying systems.
- Develop methods to map time-varying effects to generalized frequency response functions (FRFs).
- Enable tracking of nonlinear frequency phenomena like intermodulation and energy transfer.
Main Methods:
- Utilized parametric time-varying nonlinear autoregressive with exogenous input (NLARX) models.
- Developed a mapping to generalized frequency response functions (FRFs) to represent time-varying effects.
- Introduced a new mapping for the nonlinear output FRF.
Main Results:
- Demonstrated the ability to track nonlinear features in the frequency domain.
- Successfully mapped time-varying system dynamics to generalized FRFs.
- Illustrated the framework's effectiveness with simulated data and real intracranial electroencephalogram (EEG) data.
Conclusions:
- The proposed framework provides a robust method for analyzing nonlinear time-varying systems.
- The generalized FRFs effectively capture complex frequency-dependent behaviors.
- The approach is applicable to analyzing biological signals like EEG data.
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