Fourier transform (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Fourier transform" in English language version.

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Howe 1980. Howe, Roger (1980), "On the role of the Heisenberg group in harmonic analysis", Bulletin of the American Mathematical Society, 3 (2): 821–844, doi:10.1090/S0273-0979-1980-14825-9, MR 0578375
Howe 1980 Howe, Roger (1980), "On the role of the Heisenberg group in harmonic analysis", Bulletin of the American Mathematical Society, 3 (2): 821–844, doi:10.1090/S0273-0979-1980-14825-9, MR 0578375
Hewitt & Ross 1970, Chapter 8 Hewitt, Edwin; Ross, Kenneth A. (1970), Abstract harmonic analysis, Die Grundlehren der mathematischen Wissenschaften, Band 152, vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Springer, MR 0262773

archive.org

In relativistic quantum mechanics one encounters vector-valued Fourier transforms of multi-component wave functions. In quantum field theory, operator-valued Fourier transforms of operator-valued functions of spacetime are in frequent use, see for example Greiner & Reinhardt (1996). Greiner, W.; Reinhardt, J. (1996), Field Quantization, Springer, ISBN 978-3-540-59179-5
Oppenheim, Schafer & Buck 1999, p. 58 Oppenheim, Alan V.; Schafer, Ronald W.; Buck, John R. (1999), Discrete-time signal processing (2nd ed.), Upper Saddle River, N.J.: Prentice Hall, ISBN 0-13-754920-2
Proakis, John G.; Manolakis, Dimitris G. (1996). Digital Signal Processing: Principles, Algorithms, and Applications (3rd ed.). Prentice Hall. p. 291. ISBN 978-0-13-373762-2.

arxiv.org

Celeghini, Gadella & del Olmo 2021 Celeghini, Enrico; Gadella, Manuel; del Olmo, Mariano A. (2021), "Hermite Functions and Fourier Series", Symmetry, 13 (5): 853, arXiv:2007.10406, Bibcode:2021Symm...13..853C, doi:10.3390/sym13050853
Grafakos & Teschl 2013 Grafakos, Loukas; Teschl, Gerald (2013), "On Fourier transforms of radial functions and distributions", J. Fourier Anal. Appl., 19 (1): 167–179, arXiv:1112.5469, Bibcode:2013JFAA...19..167G, doi:10.1007/s00041-012-9242-5, S2CID 1280745

bnf.fr

gallica.bnf.fr

Poincaré 1895, p. 102 Poincaré, Henri (1895), Théorie analytique de la propagation de la chaleur, Paris: Carré

books.google.com

Pinsky 2002, p. 91. Pinsky, Mark (2002), Introduction to Fourier Analysis and Wavelets, Brooks/Cole, ISBN 978-0-534-37660-4
Fourier 1822, p. 525 Fourier, J.B. Joseph (1822), Théorie analytique de la chaleur (in French), Paris: Firmin Didot, père et fils, OCLC 2688081
Fourier 1878, p. 408 Fourier, J.B. Joseph (1878) [1822], The Analytical Theory of Heat, translated by Alexander Freeman, The University Press (translated from French)
Rahman 2011, p. 10. Rahman, Matiur (2011), Applications of Fourier Transforms to Generalized Functions, WIT Press, ISBN 978-1-84564-564-9
Kaiser 1994, p. 29 Kaiser, Gerald (1994), "A Friendly Guide to Wavelets", Physics Today, 48 (7): 57–58, Bibcode:1995PhT....48g..57K, doi:10.1063/1.2808105, ISBN 978-0-8176-3711-8
Rahman 2011, p. 11 Rahman, Matiur (2011), Applications of Fourier Transforms to Generalized Functions, WIT Press, ISBN 978-1-84564-564-9
Fourier 1822 Fourier, J.B. Joseph (1822), Théorie analytique de la chaleur (in French), Paris: Firmin Didot, père et fils, OCLC 2688081
Pinsky 2002 Pinsky, Mark (2002), Introduction to Fourier Analysis and Wavelets, Brooks/Cole, ISBN 978-0-534-37660-4
Stein & Weiss 1971 Stein, Elias; Weiss, Guido (1971), Introduction to Fourier Analysis on Euclidean Spaces, Princeton, N.J.: Princeton University Press, ISBN 978-0-691-08078-9
Pinsky 2002, chpt. 2.4.3 The Uncertainty Principle Pinsky, Mark (2002), Introduction to Fourier Analysis and Wavelets, Brooks/Cole, ISBN 978-0-534-37660-4
Stein & Shakarchi 2003, chpt. 5.4 The Heisenberg uncertainty principle Stein, Elias; Shakarchi, Rami (2003), Fourier Analysis: An introduction, Princeton University Press, ISBN 978-0-691-11384-5
Chatfield 2004, p. 113 Chatfield, Chris (2004), The Analysis of Time Series: An Introduction, Texts in Statistical Science (6th ed.), London: Chapman & Hall/CRC, ISBN 9780203491683
Fourier 1822, p. 441 Fourier, J.B. Joseph (1822), Théorie analytique de la chaleur (in French), Paris: Firmin Didot, père et fils, OCLC 2688081
Stein & Weiss 1971, pp. 1–2. Stein, Elias; Weiss, Guido (1971), Introduction to Fourier Analysis on Euclidean Spaces, Princeton, N.J.: Princeton University Press, ISBN 978-0-691-08078-9
Stein & Weiss 1971, Thm. 2.3. Stein, Elias; Weiss, Guido (1971), Introduction to Fourier Analysis on Euclidean Spaces, Princeton, N.J.: Princeton University Press, ISBN 978-0-691-08078-9
Pinsky 2002, p. 256. Pinsky, Mark (2002), Introduction to Fourier Analysis and Wavelets, Brooks/Cole, ISBN 978-0-534-37660-4
Knapp 2001 Knapp, Anthony W. (2001), Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton University Press, ISBN 978-0-691-09089-4
Stein & Weiss 1971, Thm. IV.3.3 Stein, Elias; Weiss, Guido (1971), Introduction to Fourier Analysis on Euclidean Spaces, Princeton, N.J.: Princeton University Press, ISBN 978-0-691-08078-9
Easton 2010 Easton, Roger L. Jr. (2010), Fourier Methods in Imaging, John Wiley & Sons, ISBN 978-0-470-68983-7, retrieved 26 May 2020
Stein & Weiss 1971, Thm. 4.15 Stein, Elias; Weiss, Guido (1971), Introduction to Fourier Analysis on Euclidean Spaces, Princeton, N.J.: Princeton University Press, ISBN 978-0-691-08078-9
Stein & Weiss 1971, p. 6 Stein, Elias; Weiss, Guido (1971), Introduction to Fourier Analysis on Euclidean Spaces, Princeton, N.J.: Princeton University Press, ISBN 978-0-691-08078-9

doi.org

Khare, Butola & Rajora 2023, pp. 13–14 Khare, Kedar; Butola, Mansi; Rajora, Sunaina (2023), "Chapter 2.3 Fourier Transform as a Limiting Case of Fourier Series", Fourier Optics and Computational Imaging (2nd ed.), Springer, doi:10.1007/978-3-031-18353-9, ISBN 978-3-031-18353-9, S2CID 255676773
Kaiser 1994, p. 29 Kaiser, Gerald (1994), "A Friendly Guide to Wavelets", Physics Today, 48 (7): 57–58, Bibcode:1995PhT....48g..57K, doi:10.1063/1.2808105, ISBN 978-0-8176-3711-8
Stade 2005, pp. 298–299. Stade, Eric (2005). Fourier Analysis. Wiley. doi:10.1002/9781118165508. ISBN 978-0-471-66984-5.
Howe 1980. Howe, Roger (1980), "On the role of the Heisenberg group in harmonic analysis", Bulletin of the American Mathematical Society, 3 (2): 821–844, doi:10.1090/S0273-0979-1980-14825-9, MR 0578375
Wolf 1979, p. 307ff Wolf, Kurt B. (1979), Integral Transforms in Science and Engineering, Springer, doi:10.1007/978-1-4757-0872-1, ISBN 978-1-4757-0874-5
Celeghini, Gadella & del Olmo 2021 Celeghini, Enrico; Gadella, Manuel; del Olmo, Mariano A. (2021), "Hermite Functions and Fourier Series", Symmetry, 13 (5): 853, arXiv:2007.10406, Bibcode:2021Symm...13..853C, doi:10.3390/sym13050853
Condon 1937 Condon, E. U. (1937), "Immersion of the Fourier transform in a continuous group of functional transformations", Proc. Natl. Acad. Sci., 23 (3): 158–164, Bibcode:1937PNAS...23..158C, doi:10.1073/pnas.23.3.158, PMC 1076889, PMID 16588141
Wolf 1979, p. 320 Wolf, Kurt B. (1979), Integral Transforms in Science and Engineering, Springer, doi:10.1007/978-1-4757-0872-1, ISBN 978-1-4757-0874-5
Wolf 1979, p. 312 Wolf, Kurt B. (1979), Integral Transforms in Science and Engineering, Springer, doi:10.1007/978-1-4757-0872-1, ISBN 978-1-4757-0874-5
Howe 1980 Howe, Roger (1980), "On the role of the Heisenberg group in harmonic analysis", Bulletin of the American Mathematical Society, 3 (2): 821–844, doi:10.1090/S0273-0979-1980-14825-9, MR 0578375
Widder & Wiener 1938, p. 537 Widder, David Vernon; Wiener, Norbert (August 1938), "Remarks on the Classical Inversion Formula for the Laplace Integral", Bulletin of the American Mathematical Society, 44 (8): 573–575, doi:10.1090/s0002-9904-1938-06812-7
Grafakos & Teschl 2013 Grafakos, Loukas; Teschl, Gerald (2013), "On Fourier transforms of radial functions and distributions", J. Fourier Anal. Appl., 19 (1): 167–179, arXiv:1112.5469, Bibcode:2013JFAA...19..167G, doi:10.1007/s00041-012-9242-5, S2CID 1280745
Mallat 2009, p. 45. Mallat, Stéphane (2009), A wavelet tour of signal processing: the sparse way, Amsterdam Boston: Elsevier/Academic Press, doi:10.1016/B978-0-12-374370-1.X0001-8, ISBN 978-0-12-374370-1
Edwards 1982, pp. 53, 67, 72–73. Edwards, R. E. (1982). Fourier Series. Vol. 85. New York, NY: Springer New York. doi:10.1007/978-1-4613-8156-3. ISBN 978-1-4613-8158-7.
Edwards 1982, p. 53. Edwards, R. E. (1982). Fourier Series. Vol. 85. New York, NY: Springer New York. doi:10.1007/978-1-4613-8156-3. ISBN 978-1-4613-8158-7.
Correia, L. B.; Justo, J. F.; Angélico, B. A. (2024). "Polynomial Adaptive Synchrosqueezing Fourier Transform: A method to optimize multiresolution". Digital Signal Processing. 150: 104526. Bibcode:2024DSPRJ.15004526C. doi:10.1016/j.dsp.2024.104526.
Bailey & Swarztrauber 1994 Bailey, David H.; Swarztrauber, Paul N. (1994), "A fast method for the numerical evaluation of continuous Fourier and Laplace transforms" (PDF), SIAM Journal on Scientific Computing, 15 (5): 1105–1110, Bibcode:1994SJSC...15.1105B, CiteSeerX 10.1.1.127.1534, doi:10.1137/0915067, archived from the original (PDF) on 2008-07-20, retrieved 2017-11-01
Lado 1971 Lado, F. (1971), "Numerical Fourier transforms in one, two, and three dimensions for liquid state calculations", Journal of Computational Physics, 8 (3): 417–433, Bibcode:1971JCoPh...8..417L, doi:10.1016/0021-9991(71)90021-0
Simonen & Olkkonen 1985 Simonen, P.; Olkkonen, H. (1985), "Fast method for computing the Fourier integral transform via Simpson's numerical integration", Journal of Biomedical Engineering, 7 (4): 337–340, doi:10.1016/0141-5425(85)90067-6, PMID 4057997

doverpublications.com

store.doverpublications.com

Kolmogorov & Fomin 1999 Kolmogorov, Andrey Nikolaevich; Fomin, Sergei Vasilyevich (1999) [1957], Elements of the Theory of Functions and Functional Analysis, Dover (translated from Russian)

harvard.edu

ui.adsabs.harvard.edu

Kaiser 1994, p. 29 Kaiser, Gerald (1994), "A Friendly Guide to Wavelets", Physics Today, 48 (7): 57–58, Bibcode:1995PhT....48g..57K, doi:10.1063/1.2808105, ISBN 978-0-8176-3711-8
Celeghini, Gadella & del Olmo 2021 Celeghini, Enrico; Gadella, Manuel; del Olmo, Mariano A. (2021), "Hermite Functions and Fourier Series", Symmetry, 13 (5): 853, arXiv:2007.10406, Bibcode:2021Symm...13..853C, doi:10.3390/sym13050853
Condon 1937 Condon, E. U. (1937), "Immersion of the Fourier transform in a continuous group of functional transformations", Proc. Natl. Acad. Sci., 23 (3): 158–164, Bibcode:1937PNAS...23..158C, doi:10.1073/pnas.23.3.158, PMC 1076889, PMID 16588141
Grafakos & Teschl 2013 Grafakos, Loukas; Teschl, Gerald (2013), "On Fourier transforms of radial functions and distributions", J. Fourier Anal. Appl., 19 (1): 167–179, arXiv:1112.5469, Bibcode:2013JFAA...19..167G, doi:10.1007/s00041-012-9242-5, S2CID 1280745
Correia, L. B.; Justo, J. F.; Angélico, B. A. (2024). "Polynomial Adaptive Synchrosqueezing Fourier Transform: A method to optimize multiresolution". Digital Signal Processing. 150: 104526. Bibcode:2024DSPRJ.15004526C. doi:10.1016/j.dsp.2024.104526.
Bailey & Swarztrauber 1994 Bailey, David H.; Swarztrauber, Paul N. (1994), "A fast method for the numerical evaluation of continuous Fourier and Laplace transforms" (PDF), SIAM Journal on Scientific Computing, 15 (5): 1105–1110, Bibcode:1994SJSC...15.1105B, CiteSeerX 10.1.1.127.1534, doi:10.1137/0915067, archived from the original (PDF) on 2008-07-20, retrieved 2017-11-01
Lado 1971 Lado, F. (1971), "Numerical Fourier transforms in one, two, and three dimensions for liquid state calculations", Journal of Computational Physics, 8 (3): 417–433, Bibcode:1971JCoPh...8..417L, doi:10.1016/0021-9991(71)90021-0

lbl.gov

crd.lbl.gov

Bailey & Swarztrauber 1994 Bailey, David H.; Swarztrauber, Paul N. (1994), "A fast method for the numerical evaluation of continuous Fourier and Laplace transforms" (PDF), SIAM Journal on Scientific Computing, 15 (5): 1105–1110, Bibcode:1994SJSC...15.1105B, CiteSeerX 10.1.1.127.1534, doi:10.1137/0915067, archived from the original (PDF) on 2008-07-20, retrieved 2017-11-01

mit.edu

direct.mit.edu

Wiener 1949 Wiener, Norbert (1949). Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications. MIT Press. ISBN 9780262257190.

ncsu.edu

lib.ncsu.edu

Lado 1971 Lado, F. (1971), "Numerical Fourier transforms in one, two, and three dimensions for liquid state calculations", Journal of Computational Physics, 8 (3): 417–433, Bibcode:1971JCoPh...8..417L, doi:10.1016/0021-9991(71)90021-0

nih.gov

pubmed.ncbi.nlm.nih.gov

Condon 1937 Condon, E. U. (1937), "Immersion of the Fourier transform in a continuous group of functional transformations", Proc. Natl. Acad. Sci., 23 (3): 158–164, Bibcode:1937PNAS...23..158C, doi:10.1073/pnas.23.3.158, PMC 1076889, PMID 16588141
Simonen & Olkkonen 1985 Simonen, P.; Olkkonen, H. (1985), "Fast method for computing the Fourier integral transform via Simpson's numerical integration", Journal of Biomedical Engineering, 7 (4): 337–340, doi:10.1016/0141-5425(85)90067-6, PMID 4057997

ncbi.nlm.nih.gov

Condon 1937 Condon, E. U. (1937), "Immersion of the Fourier transform in a continuous group of functional transformations", Proc. Natl. Acad. Sci., 23 (3): 158–164, Bibcode:1937PNAS...23..158C, doi:10.1073/pnas.23.3.158, PMC 1076889, PMID 16588141

projecteuclid.org

Widder & Wiener 1938, p. 537 Widder, David Vernon; Wiener, Norbert (August 1938), "Remarks on the Classical Inversion Formula for the Laplace Integral", Bulletin of the American Mathematical Society, 44 (8): 573–575, doi:10.1090/s0002-9904-1938-06812-7

psu.edu

citeseerx.ist.psu.edu

Bailey & Swarztrauber 1994 Bailey, David H.; Swarztrauber, Paul N. (1994), "A fast method for the numerical evaluation of continuous Fourier and Laplace transforms" (PDF), SIAM Journal on Scientific Computing, 15 (5): 1105–1110, Bibcode:1994SJSC...15.1105B, CiteSeerX 10.1.1.127.1534, doi:10.1137/0915067, archived from the original (PDF) on 2008-07-20, retrieved 2017-11-01

semanticscholar.org

api.semanticscholar.org

Khare, Butola & Rajora 2023, pp. 13–14 Khare, Kedar; Butola, Mansi; Rajora, Sunaina (2023), "Chapter 2.3 Fourier Transform as a Limiting Case of Fourier Series", Fourier Optics and Computational Imaging (2nd ed.), Springer, doi:10.1007/978-3-031-18353-9, ISBN 978-3-031-18353-9, S2CID 255676773
Grafakos & Teschl 2013 Grafakos, Loukas; Teschl, Gerald (2013), "On Fourier transforms of radial functions and distributions", J. Fourier Anal. Appl., 19 (1): 167–179, arXiv:1112.5469, Bibcode:2013JFAA...19..167G, doi:10.1007/s00041-012-9242-5, S2CID 1280745

stanford.edu

statweb.stanford.edu

"Applied Fourier Analysis and Elements of Modern Signal Processing Lecture 3" (PDF). January 12, 2016. Retrieved 2019-10-11.

thefouriertransform.com

"The Integration Property of the Fourier Transform". The Fourier Transform .com. 2015 [2010]. Archived from the original on 2022-01-26. Retrieved 2023-08-20.

ucdavis.edu

math.ucdavis.edu

Hunter 2014. Hunter, J.K. (2014), "Appendix: The Fourier transform", Lecture Notes on PDEs, retrieved January 12, 2025

unam.mx

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Wolf 1979, p. 307ff Wolf, Kurt B. (1979), Integral Transforms in Science and Engineering, Springer, doi:10.1007/978-1-4757-0872-1, ISBN 978-1-4757-0874-5
Wolf 1979, p. 320 Wolf, Kurt B. (1979), Integral Transforms in Science and Engineering, Springer, doi:10.1007/978-1-4757-0872-1, ISBN 978-1-4757-0874-5
Wolf 1979, p. 312 Wolf, Kurt B. (1979), Integral Transforms in Science and Engineering, Springer, doi:10.1007/978-1-4757-0872-1, ISBN 978-1-4757-0874-5

web.archive.org

Bailey & Swarztrauber 1994 Bailey, David H.; Swarztrauber, Paul N. (1994), "A fast method for the numerical evaluation of continuous Fourier and Laplace transforms" (PDF), SIAM Journal on Scientific Computing, 15 (5): 1105–1110, Bibcode:1994SJSC...15.1105B, CiteSeerX 10.1.1.127.1534, doi:10.1137/0915067, archived from the original (PDF) on 2008-07-20, retrieved 2017-11-01
"The Integration Property of the Fourier Transform". The Fourier Transform .com. 2015 [2010]. Archived from the original on 2022-01-26. Retrieved 2023-08-20.

worldcat.org

search.worldcat.org

Fourier 1822, p. 525 Fourier, J.B. Joseph (1822), Théorie analytique de la chaleur (in French), Paris: Firmin Didot, père et fils, OCLC 2688081
Fourier 1822 Fourier, J.B. Joseph (1822), Théorie analytique de la chaleur (in French), Paris: Firmin Didot, père et fils, OCLC 2688081
Fourier 1822, p. 441 Fourier, J.B. Joseph (1822), Théorie analytique de la chaleur (in French), Paris: Firmin Didot, père et fils, OCLC 2688081