A new form of discrete real Fourier transform and its potential applications

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Annals of Mathematics and Physics volume5-issue2 articles
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Submitted: November 1, 2022
Published: Nov 24, 2022
DOI: 10.17352/amp.000060

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Grzegorz Plewa*
National Centre for Nuclear Research, Interdisciplinary Division for Energy Analyses, Wolodyjowskiego 83, 02-724, Warsaw, Poland

Abstract

The paper will present a new version of a real discrete Fourier transform, based on a symmetric frequencies combination of sine and cosine functions. Basic aspects of the construction as well as the potential applications will be discussed. This will include elements of the standard Fourier analysis as well as applications to the class of differential equations in string theory.

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Article Details

Plewa, G. (2022). A new form of discrete real Fourier transform and its potential applications. Annals of Mathematics and Physics, 5(2), 160–166. https://doi.org/10.17352/amp.000060
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Copyright (c) 2022 Plewa G.

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

Bailey DH, Swarztrauber PN. A Fast Method for the Numerical Evaluation of Continuous Fourier and Laplace Transforms. Scientific Computing. 1993; 15:1105-11010.

Ersoy OK, Hu NC. Fast algorithms for the real discrete Fourier transform, CASSP-88., International Conference on Acoustics, Speech and Signal Processing. 1988; 3:1902-1905.

Wilson R, Calway AD, Pearson ERS. A generalized wavelet transform for Fourier analysis: the multiresolution Fourier transform and its application to image and audio signal analysis. IEEE Transactions on Information Theory. 1992; 38.

Valluri SR, Dergachev V, Zhang X, Chishtie FA. Fourier transform of the continuous gravitational wave signal, Phys. Rev. D. 2021; 104:024065.

Weinberg S. The Quantum theory of fields. Foundations, Cambridge University Press. 2005; 1.

Srednicki M. Quantum field theory, Cambridge University Press. 2007.

Góźdź A, Piechocki W, Plewa G, Trześniewski T. Universe. 2021; 7:49. 2003.03990.

Maldacena JM. The Large N limit of superconformal field theories and supergravity. Int. J. Theor. Phys. 1999; 38:1113-1133; 9711200.

Hubeny VE. The AdS/CFT Correspondence. Class. Quant. Grav. 2009; 2015:32; 124010.

Susskind L. The World as a hologram. J. Math. Phys. 1995; 36:6377-6396; 1305.3182.

Ryu S. Tadashi Takayanagi Holographic derivation of entanglement entropy from AdS/CFT. Phys. Rev. Lett. 2006; 96:181602:0603001.

Blanco DD. Horacio Casini Ling-Yan Hung Robert C Myers, Relative Entropy and Holography. JHEP. 2013; 08:060;1305.3182.

Grandclement P, Novak J. Spectral methods for numerical relativity. Living Rev. Rel. 2009; 12:0706.2286.

Janik RA, Plewa G, Soltanpanahi H. Michal Spalinski Linearized nonequilibrium dynamics in nonconformal plasma, Phys. Rev. D. 2015; 91:126013; 1503.07149.