Article: Verification of congruency and coherence of Fourier, Laplace, and Z-transformations Journal: International Journal of Student Project Reporting (IJSPR) 2022 Vol.1 No.2 pp.99 - 122 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. Inderscience Publishers - linking academia, business and industry through research

Title: Verification of congruency and coherence of Fourier, Laplace, and Z-transformations

Authors: Klejda Kumi; Regi Berisha; Xhesika Biçaku; Raziena Uruçi; Carlo Ciulla

Addresses: Department of Computer Engineering, Epoka University, Rr. Tiranë-Rinas, Km. 12, 1032, Vorë, Tirana, Albania ' Department of Computer Engineering, Epoka University, Rr. Tiranë-Rinas, Km. 12, 1032, Vorë, Tirana, Albania ' Department of Computer Engineering, Epoka University, Rr. Tiranë-Rinas, Km. 12, 1032, Vorë, Tirana, Albania ' Department of Computer Engineering, Epoka University, Rr. Tiranë-Rinas, Km. 12, 1032, Vorë, Tirana, Albania ' Department of Computer Engineering, Epoka University, Rr. Tiranë-Rinas, Km. 12, 1032, Vorë, Tirana, Albania

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 e^jω 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.

Keywords: Fourier; Laplace; Z-transformation; k-space; phase.

DOI: 10.1504/IJSPR.2022.128755

International Journal of Student Project Reporting, 2022 Vol.1 No.2, pp.99 - 122

Received: 14 May 2021
Accepted: 19 Jul 2021
Published online: 02 Feb 2023 *

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Title: Verification of congruency and coherence of Fourier, Laplace, and Z-transformations

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