Audio signal approximation and fuzzy logic-based acoustic noise-risk assessment using Fourier–Dirichlet analysis and hyperbolic series representations

Yogeesh Nijalingappa
Department of Mathematics, Government First Grade College, Tumkur 572102, India; Mathematics & Natural Sciences, Gulf University for Science & Technology, Hawalli 32093, Kuwait; Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Asokan Vasudevan
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Soon Eu Hui
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Zetty Pakir Mastan
Faculty of Engineering and Quantity Surveying, INTI International University, Nilai 71800, Malaysia
Choo Wou Onn
International Relations and Collaborations Centre, INTI International University, Nilai 71800, Malaysia
Mohammed Almakki
School of Engineering, Architecture and Interior Design, Amity University Dubai, Dubai P.O. Box 345019, United Arab Emirates

Article ID: 4180

Keywords: Fourier series; Dirichlet conditions; audio signal approximation; hyperbolic series; fuzzy logic; acoustic noise-risk assessment; Mamdani fuzzy inference; harmonic analysis

Abstract

This paper presents an acoustics-oriented study that combines classical Fourier–Dirichlet signal approximation with a fuzzy logic-based noise-risk interpretation layer. The harmonic-analysis part revisits Fourier series for periodic and quasi-periodic audio waveforms under classical Dirichlet conditions and restates these conditions in a form that is practically checkable on sampled audio segments; no new convergence theorem is claimed. A complementary hyperbolic-series representation is used as an illustrative analytical tool for discussing compact representations of selected waveform classes. The applied contribution of the paper is a Mamdani fuzzy inference system that converts uncertain acoustic measurements into an interpretable Noise-Risk Index using A-weighted equivalent sound level, daily exposure duration, and source–receiver distance. The fuzzy model uses triangular/trapezoidal memberships, an interpretable rule base, min–max inference, and centroid defuzzification. To show the practical usefulness in sound and vibration practice, one waveform-reconstruction example and a twelve-scenario acoustic-risk dataset with regard to traffic, workshop, generator room, and public address contexts are reported in the study. The resulting fuzzy system generates a range of risk scores from 22 to 92, lying within the safe, caution, high, and critical level categories and depicts smooth transitions as we approach decision boundaries where a crisp threshold can often be challenging to decode. This work thus establishes Fourier analysis as the underlying level for acoustic signals and fuzzy inference as a decision-support level in the context of uncertainty-based exposure assessment. The current coupling is linear instead of feature-driven: the Fourier-based signal description forms the basis for exposure descriptors, and the fuzzy system processes these descriptors given uncertainty.

Published

2026-07-24

How to Cite

Nijalingappa, Y., Vasudevan, A., Hui, S. E., Mastan, Z. P., Onn, C. W., & Almakki, M. (2026). Audio signal approximation and fuzzy logic-based acoustic noise-risk assessment using Fourier–Dirichlet analysis and hyperbolic series representations. Sound & Vibration, 60(5). https://doi.org/10.59400/sv4180

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Vol. 60 No. 5 (2026): In Progress

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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Audio signal approximation and fuzzy logic-based acoustic noise-risk assessment using Fourier–Dirichlet analysis and hyperbolic series representations

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