[Submitted on 24 Feb 2026 (v1), last revised 20 Jul 2026 (this version, v2)]

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Abstract:Segmented curve fitting remains an essential approach for the comprehensive analysis of local patterns in non-stationary time-series data. However, traditional regression algorithms primarily focus on linear or polynomial functions, which can be insufficient for analyzing raw signals with oscillatory or transcendental behavior. In this paper, we propose Segmented Continuous Optimization (SCO), a framework that performs piecewise continuous curve fitting on various non-linear models, including trigonometric, polynomial, and exponential. SCO presents a novel signal representation by optimizing a user-defined model in segments with $C^1$ continuity to properly analyze the data's local and global trends. The framework is tested for accuracy and efficiency across all included models. Finally, we provide examples using velocity and EEG datasets to demonstrate the algorithm's practical usage in examining signal patterns, optimized parameters, derivatives, and integrals of the final fit.

Submission history

From: Teymur Aghayev [view email]
[v1] Tue, 24 Feb 2026 12:58:21 UTC (1,951 KB)
[v2] Mon, 20 Jul 2026 07:35:16 UTC (997 KB)

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