Determination of Envelopes of Real Finite Discrete Signals Based on Discrete Fourier Transforms with Variable Parameters

In numerous scientific disciplines, the advancement of digital Fourier processing-its theory, methods, and algorithms-is pivotal in addressing a spectrum of theoretical and practical challenges. This article introduces a novel approach to defining envelopes of real, finite discrete signals, leveraging a new class of unitary discrete Fourier transforms. These transforms, distinguished by their adaptability, are introduced, explored, and designated by the authors as discrete Fourier transforms with variable parameters. The paper expands the theory, methods, and algorithms for determining the envelopes of two-dimensional, discrete, finite real signals, utilizing these variable-parameter Fourier transforms. The theoretical findings are substantiated through numerical modeling, with illustrative examples using test signals. This work should be viewed as an extension of the theory, methods, and algorithms pertaining to digital Fourier processing of both real and complex finite discrete signals.