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The Use of Functionals in the Analysis of Non-linear Physical Systems†
Abstract
This report is an attempt to develop a method of analysis applicable equally to linear or non-linear systems. The main method discussed is the expansion of the input-output relation in a functional power series–an idea first due to Volterra for general functional relationships and to Wiener in its application to non-linear communication problems. The report attempts to present a systematic development of this idea. The last part of the report discusses analogous expansions in a series of terms orthogonal with respect to input statistics.
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Citations
Cited by
Fading memory and the problem of approximating nonlinear operators with Volterra series
Boyd, S., & Chua, L. (1985) · IEEE Transactions on Circuits and Systems · doi:10.1109/tcs.1985.1085649 · Cited by 991
An algebraic approach to nonlinear functional expansions
Fliess, M., Lamnabhi, M., & Lamnabhi-Lagarrigue, F. (1983) · IEEE Transactions on Circuits and Systems · doi:10.1109/tcs.1983.1085397 · Cited by 274
Modeling methology for nonlinear physiological systems
Marmarelis, V. Z. (1997) · Annals of Biomedical Engineering · doi:10.1007/bf02648038 · Cited by 94
Metadata
- Authors
- BARRETT, J. F.
- Venue
- Journal of Electronics and Control
- Publisher
- Informa UK Limited
- Published
- 1963-12
- Volume
- 15
- Issue
- 6
- Pages
- 567-615
- ISSN
- 0368-1947 (ISSN-L)
- OpenAlex
- W1982585638
- Cited by
- 216
- References
- 0
- FWCI
- 10.02
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: The Use of Functionals in the Analysis of Non-linear Physical Systems†. https://app.cochat.ai/papers/10.1080/00207216308937611
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- BARRETT, J. F. (1963). The Use of Functionals in the Analysis of Non-linear Physical Systems†. Journal of Electronics and Control. https://doi.org/10.1080/00207216308937611
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
