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@article{196837,
        author = {G.Subashini and Shrikanth S},
        title = {Dominant Periodic Component Extraction in Finite Signals Using a Discrete Fourier Series Framework: Theory, Reconstruction, and Motor Fault Validation},
        journal = {International Journal of Innovative Research in Technology},
        year = {2026},
        volume = {12},
        number = {11},
        pages = {5203-5212},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=196837},
        abstract = {Finite discrete signals frequently contain periodic structure that reflects the underlying physical behavior of a system. In practical observations, however, this structure is often obscured by noise, drift, overlapping oscillatory components, and finite-window effects. This paper develops a mathematical framework for dominant periodic component extraction in finite signals using the Discrete Fourier Series (DFS). Starting from discrete trigonometric orthogonality, explicit coefficient expressions are derived through projection. A magnitude-based selection rule is then introduced to identify dominant frequency components, followed by a neighborhood refinement mechanism that accounts for finite-window spectral spreading. The selected dominant components are subsequently used to reconstruct an interpretable periodic signal together with a complementary residual. The development is presented in a step-by-step manner so that the problem statement, the derivation, and the final equations remain mathematically clear. The framework is validated using real motor-bearing vibration data under healthy, inner-race, ball, and outer-race fault conditions. Both visual comparisons and quantitative metrics show that faulty signals exhibit significantly stronger dominant periodic structure than the healthy condition. The proposed DFS framework therefore provides a mathematically transparent and practically useful approach for interpreting periodic mechanisms in real vibration signals.},
        keywords = {Discrete Fourier Series, finite signals, dominant periodic component extraction, mathematical signal analysis, frequency-domain reconstruction, motor fault diagnosis, bearing vibration.},
        month = {April},
        }