Document Type
Conference Paper
Publication Date
2024
DOI
10.1016/j.ifacol.2024.10.199
Publication Title
IFAC-PapersOnline
Volume
58
Issue
17
Pages
380-385
Conference Name
26th International Symposium on Mathematical Theory of Networks and Systems MTNS 2024, 19-23 August, 2024, Cambridge, United Kingdom
Abstract
We collect three instances where the theory of generalized functions may still make contributions to the study of signals and systems. In the first, a purely algebraic approach is presented for LTI-ODE's, in terms of two operators, D and T, respectively the differentiation operator and the multiplication-by-the-independent-variable operator. This formalism adds simplicity, a duality theory, and nicely generalizes to other classes of operator equations and their solutions. In the second part we extend the classical bilateral Laplace transform to include Bohl functions with support in ℝ by invoking Sato's hyperfunctions. Finally, in the third case we use the Colombeau algebra to allow for products of generalized functions. This is important in the study of (smooth) nonlinear systems driven by impulsive inputs, and hybrid system theory.
Rights
© 2024 The Authors.
This is an open access article under the Creative Commons Attribution-NonCommercial-Noderivatives 4.0 International (CC-BY-NC-ND 4.0) License.
Original Publication Citation
Verriest, E. I., Dirr, G., & Gray, W. S. (2024). Generalized functions in the study of signals and systems. IFAC-PapersOnLine, 58(17), 380-385. https://doi.org/10.1016/j.ifacol.2024.10.199
Repository Citation
Verriest, Erik I.; Dirr, Gunther; and Gray, W. Steven, "Generalized Functions in the Study of Signals and Systems" (2024). Electrical & Computer Engineering Faculty Publications. 493.
https://digitalcommons.odu.edu/ece_fac_pubs/493