A Unified Study of Modulation and Parseval Relations for Two-Dimensional Fractional Sine Transforms

Sharma, V. A.

doi:https://doi.org/10.55041/ijcope.v2i8.195

Volume 02, Issue 8

Published on: August 2026

A UNIFIED STUDY OF MODULATION AND PARSEVAL RELATIONS FOR TWO-DIMENSIONAL FRACTIONAL SINE TRANSFORMS

V. A. Sharma

Department of Mathematics, Smt. Narsamma Arts, Commerce and Science college, Amravati 444606

DOI:https://doi.org/10.55041/ijcope.v2i8.195

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Abstract

As the sine transform, cosine transform and Hartley transform are widely used in signal processing, the application of their fractional versions in signal and image processing is very promising. In this paper the distributional generalized two-dimensional fractional sine transform is studied. The modulation theorem for a product of sines is established: the transform is expressed as a linear combination of four fractional cosine transforms of a modulated version of the original function, evaluated at shifted frequency points. An auxiliary angle that equates quadratic-phase coefficients is identified. Parseval’s relation is recorded. The operational properties are applied to spectral analysis of multi-scale supply-chain dynamics, residue-based resonance extraction in hybrid-vehicle systems, shift-invariant multi-echelon lead-time analysis, exponential modulation for secure digital supply-chain networks, and energy-preserving resilience metrics, consistent with the frameworks developed in the cited literature. Recommendations for future discrete, numerical and hybrid-transform research are provided.

Keywords— fractional sine transform, modulation theorem, Parseval’s relation, two-dimensional transforms, supply-chain spectral analysis, hybrid-vehicle resonance, secure digital networks, resilient logistics, future work.

How to Cite this Paper

Sharma, V. A. (2026). A Unified Study of Modulation and Parseval Relations for Two-Dimensional Fractional Sine Transforms. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-9. https://doi.org/10.55041/ijcope.v2i8.195

Sharma, V.. "A Unified Study of Modulation and Parseval Relations for Two-Dimensional Fractional Sine Transforms." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 8, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i8.195.

Sharma, V.. "A Unified Study of Modulation and Parseval Relations for Two-Dimensional Fractional Sine Transforms." International Journal of Creative and Open Research in Engineering and Management 02, no. 8 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i8.195.

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References

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B. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process., vol. 42, pp. 3084–3091, 1994.

Akarshan Gulhane,“Spectral Analysis for Multi Scale Supply Chain Dynamics and Residue Based Resonance Extraction in Hybrid-Vehicle Systems,”International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.141

Akarshan Gulhane,“ Shift-Invariant Spectral Analysis of Multi-Echelon Supply-Chain Lead Times via the FKF Transform,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.136

Akarshan Gulhane,“ Spectral Framework Based on the FKF Transform for Supply Chain Dynamics and Resilience,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026,

DOI: https://doi.org/10.55041/ijcope.v2i8.140

Akarshan Gulhane,“ Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.139

Akarshan Gulhane,“ FKL Transform Key Properties, And Applications To Supply-chain Analysis,” International journal of Engineering sciences and Advanced Technology, Published:11-12-2025, Issue: Vol. 25 No. 12 (2025), Page Nos: 596-605, DOI: Https://doi.org/10.64771/ijesat.2025.v25.i12.3816

Akarshan Gulhane,“ Expanded Treatment Of The Time-Shift Property Of FKF Transform With Supply-Chain Applications,” International journal of Engineering sciences and Advanced Technology, Published:11-12-2025, Issue: Vol. 25 No. 12 (2025), Page Nos: 606 – 616,

DOI: Https://doi.org/10.64771/ijesat.2025.v25.i12.3817

Akarshan Gulhane,“ The FKF Transform: Exponential Modulation Properties And Applications To Secure Digital Supply-Chain Networks,” International journal of Engineering sciences and Advanced Technology, Published:11-12-2025, Issue: Vol. 25 No. 12 (2025), Page Nos: 617 – 623, DOI: Https://doi.org/10.64771/ijesat.2025.v25.i12.3818

Akarshan Gulhane, “Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.139.

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