Abstract :

This Paper Introduces And Systematically Develops The FKF (Fractional Kernel Fourier) Transform, A Novel Integral Transform Designed To Unify Desirable Analytic Features Of Classical Fourier Analysis With Flexible Kernel Structures Suited To Exponential Order Signals. We Provide A Complete Theoretical Treatment Of Its Fundamental Properties, With Particular Emphasis On The Exponential Modulation Property. The Exponential Modulation Property Is Expanded In Detail: If A Function F(t) Possesses An FKF Transform F(s), Then The Modulated Signal 𝑒 {𝛼 𝑡}𝑓(𝑡) Admits An FKF Transform That Is A Precise Analytic Continuation And Shift Of F(s) In The Complex Plane. Closed Form Expressions, Proofs, And Discrete Computational Realizations Are Derived. The Property Is Shown To Be Especially Powerful For Securing Time Series Data That Arise In Digital Supply-chain Networks Inventory Trajectories, Demand Signals, And Logistics Telemetry By Embedding A Controllable Exponential Carrier That Is Invertible Only With Knowledge Of The Private Modulation Parameter. A Recommended Computational Form For Discrete Data Is Presented, Together With Numerical Illustrations. Applications Demonstrate That The Combination Of FKF Transformation And Modular Arithmetic Yields Lightweight, Reversible, And Cryptographically Robust Encryption Suitable For Resource-constrained IoT Nodes Throughout Modern Supply Chains. Keywords: FKF Transform; Exponential Modulation; Integral Transforms; Discrete Computational Form; Supply-chain Cryptography; Modular Arithmetic; Secure Data Exchange; IoT Security.

Published:

11-12-2025

Issue:

Vol. 25 No. 12 (2025)

Page Nos:

617 - 623

Section:

Articles

License:

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

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