Verification of congruency and coherence of Fourier, Laplace, and Z-transformations Online publication date: Thu, 02-Feb-2023
by Klejda Kumi; Regi Berisha; Xhesika Biçaku; Raziena Uruçi; Carlo Ciulla
International Journal of Student Project Reporting (IJSPR), Vol. 1, No. 2, 2022
Abstract: This research verifies theoretically and practically, congruency and coherence of Fourier, Laplace, and Z-transformations. A dataset comprising of 24 two-dimensional images was used for experimentation. Congruency of direct and inverse Fourier, Laplace, and Z-transformations is verified based on: 1) comparison between departing images and inverse reconstructed images; 2) dissimilarity between these three transforms, quantifiable through the analysis of their frequency domain. Fourier and Laplace transforms are experimentally verified coherent when the real component of Laplace complex variable s = σ + iω is σ = 0. Fourier and Z transforms are experimentally verified coherent when the magnitude r of the complex variable z = r ejω is r = 1. The novelty of this research is the verification paradigm used to verify: 1) congruent implementation of transformations; 2) coherency across transforms. Verification assures that the software developed for this research meets the theoretical background.
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