Version 1
: Received: 21 August 2024 / Approved: 22 August 2024 / Online: 22 August 2024 (08:25:46 CEST)
How to cite:
Vasudevan, A.; N, Y.; .N, R.; D.K., G.; M, R.; J, D. Insights into Signal Behaviour: Dirichlet Problem and Hyperbolic Series Perspective with Fuzzy Approach. Preprints2024, 2024081607. https://doi.org/10.20944/preprints202408.1607.v1
Vasudevan, A.; N, Y.; .N, R.; D.K., G.; M, R.; J, D. Insights into Signal Behaviour: Dirichlet Problem and Hyperbolic Series Perspective with Fuzzy Approach. Preprints 2024, 2024081607. https://doi.org/10.20944/preprints202408.1607.v1
Vasudevan, A.; N, Y.; .N, R.; D.K., G.; M, R.; J, D. Insights into Signal Behaviour: Dirichlet Problem and Hyperbolic Series Perspective with Fuzzy Approach. Preprints2024, 2024081607. https://doi.org/10.20944/preprints202408.1607.v1
APA Style
Vasudevan, A., N, Y., .N, R., D.K., G., M, R., & J, D. (2024). Insights into Signal Behaviour: Dirichlet Problem and Hyperbolic Series Perspective with Fuzzy Approach. Preprints. https://doi.org/10.20944/preprints202408.1607.v1
Chicago/Turabian Style
Vasudevan, A., Rashmi M and Divyashree J. 2024 "Insights into Signal Behaviour: Dirichlet Problem and Hyperbolic Series Perspective with Fuzzy Approach" Preprints. https://doi.org/10.20944/preprints202408.1607.v1
Abstract
Signal approximation, is the basic idea of signal processing and mathematical analysis where complex signals can be represented with simpler ones. This paper explores unifying two mathematical fundamentals, Dirichlet-type problems, and hyperbolic series identities, into signal approximation. In this paper, we address a well-known classic topic in mathematical analysis - the Dirichlet problem - to improve (the approximation of) signal using Fourier series. We also discuss using hyperbolic series representations to increase signal modeling flexibility. In this way, we hope to create new links that span some distance along this dimension and result in a somewhat theoretical view of signal behavior - present with the mathematical rigor needed for speculation but absent from an understanding capable of appropriately handling real-world complexity. This paper provides a theoretical investigation of the mechanics at play and reveals by analogy how these mathematical tools can potentially advance signal processing techniques and understanding. This paper illustrates Fourier series and fuzzy logic methods by two case studies on signal processing, satellite communication and financial risk measurement. The first case study performs signal approximation using the Fourier series and hyperbolic function identities to provide insight into how signals behave and are modeled. The second case study deals with applying fuzzy logic for risk evaluation of investment portfolios, emphasizing the utility in evasion systems solving uncertainty and imprecision problems related to financial decisions.
Keywords
Signal Approximation; Mathematical Analysis; Fourier Series; Complex Signals; Dirichlet Problem; School; Fuzzy Logics; Hyperbolic Series Identities; Signal Processing; Signal Modelling
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
