A physical model of Fourier uncertainty principle

Department of Chemistry, University of Delhi - Delhi, 110007, India

Received: 10 December 2024
Accepted: 17 June 2025

Abstract

Fourier transform is an integral part of harmonic analysis, information theory and signal processing with wide applications. The transformation between the Fourier pair is governed by an uncertainty relation, most generally captured by the Bandwidth theorem, . The usual approaches to the uncertainty principle employ sophisticated methods which lack physical interpretation of the origin and description of the uncertainty for real systems. In this paper, we have proposed a physically inspired model of the Fourier transform with an aim to describe its underlying dynamics and how it leads to the fundamental uncertainty principle. A signal is modeled as helical spring in 3D space, which is wrapped around a circle with controllable wrapping frequency. This process is formulated to reproduce the Fourier transform. The model is used to describe the origin of uncertainty, and to formulate a new generator-based approach to the Bandwidth theorem.