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Instantaneous characterization of time-varying nonlinear systems
D Krieger1, T W Berger, R J Sclabassi
1Department of Neurological Surgery, University of Pittsburgh, PA 15213.
IEEE Transactions on Bio-Medical Engineering
|April 1, 1992
Summary
This study introduces a method to analyze how system responses change over time using functional power series (FPS) and evoked potentials (EPs). It enables instant system characterization by evaluating time-varying functions.
Area of Science:
- Systems analysis
- Signal processing
- Nonlinear dynamics
Background:
- Characterizing nonlinear systems is crucial for understanding complex behaviors.
- Functional Power Series (FPS) and Evoked Potentials (EPs) are key analytical tools.
- Assessing temporal changes in system responses is a fundamental challenge.
Purpose of the Study:
- To develop a method for analyzing time-varying responses in nonlinear systems.
- To enable dynamic characterization of systems over experimental durations.
- To provide instant system analysis at specific time points.
Main Methods:
- Computing orthogonal functional power series (FPS) from input-output cross-correlations.
- Employing regression on closed-form functions of time to model temporal variations.
- Evaluating time-varying FPS and EPs at specific time instances.
Main Results:
- Demonstrated the ability to characterize nonlinear systems with time-varying responses.
- Successfully generated time-varying FPS and EPs through regression analysis.
- Enabled instantaneous system characterization by evaluating dynamic functions.
Conclusions:
- The proposed method allows for the dynamic analysis of nonlinear systems.
- Time-varying FPS and EPs provide a means to understand system behavior evolution.
- Instantaneous evaluation offers a snapshot of system characteristics at any given moment.