Hilbert transform (English Wikipedia)

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

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ams.org

Calderón & Zygmund 1952; see Fefferman 1971. Calderón, A. P.; Zygmund, A. (1952). "On the existence of certain singular integrals". Acta Mathematica. 88 (1): 85–139. doi:10.1007/BF02392130. Fefferman, C. (1971). "Characterizations of bounded mean oscillation". Bulletin of the American Mathematical Society. 77 (4): 587–588. doi:10.1090/S0002-9904-1971-12763-5. MR 0280994.
Fefferman 1971; Fefferman & Stein 1972 Fefferman, C. (1971). "Characterizations of bounded mean oscillation". Bulletin of the American Mathematical Society. 77 (4): 587–588. doi:10.1090/S0002-9904-1971-12763-5. MR 0280994. Fefferman, C.; Stein, E. M. (1972). "H^p spaces of several variables". Acta Mathematica. 129: 137–193. doi:10.1007/BF02392215. MR 0447953.

mathscinet.ams.org

Calderón & Zygmund 1952; see Fefferman 1971. Calderón, A. P.; Zygmund, A. (1952). "On the existence of certain singular integrals". Acta Mathematica. 88 (1): 85–139. doi:10.1007/BF02392130. Fefferman, C. (1971). "Characterizations of bounded mean oscillation". Bulletin of the American Mathematical Society. 77 (4): 587–588. doi:10.1090/S0002-9904-1971-12763-5. MR 0280994.
Fefferman 1971; Fefferman & Stein 1972 Fefferman, C. (1971). "Characterizations of bounded mean oscillation". Bulletin of the American Mathematical Society. 77 (4): 587–588. doi:10.1090/S0002-9904-1971-12763-5. MR 0280994. Fefferman, C.; Stein, E. M. (1972). "H^p spaces of several variables". Acta Mathematica. 129: 137–193. doi:10.1007/BF02392215. MR 0447953.

archive.org

E.g., Stein & Weiss 1971. Stein, Elias; Weiss, Guido (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press. ISBN 0-691-08078-X.
Hilbert 1953. Hilbert, David (1953) [1912]. Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen [Framework for a General Theory of Linear Integral Equations] (in German). Leipzig & Berlin, DE (1912); New York, NY (1953): B.G. Teubner (1912); Chelsea Pub. Co. (1953). ISBN 978-3-322-00681-3. OCLC 988251080. Retrieved 2020-12-18 – via archive.org.{{cite book}}: CS1 maint: location (link)
Stein & Weiss 1971, Lemma V.2.8. Stein, Elias; Weiss, Guido (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press. ISBN 0-691-08078-X.
Stein 1970, §III.1. Stein, Elias (1970). Singular integrals and differentiability properties of functions. Princeton University Press. ISBN 0-691-08079-8.
Rabiner & Gold 1975, p. 71 (Eq 2.195) Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, N.J.: Prentice-Hall. ISBN 0-13-914101-4.
Oppenheim, Schafer & Buck 1999, p. 794-795 Oppenheim, Alan V.; Schafer, Ronald W.; Buck, John R. (1999). "11.4.1". Discrete-time signal processing (2nd ed.). Upper Saddle River, N.J.: Prentice Hall. ISBN 0-13-754920-2. The exactness of the phase of type III and IV FIR systems is a compelling motivation for their use in approximating Hilbert transformers.
Rabiner & Gold 1975, p. 172 (Fig 3.74) Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, N.J.: Prentice-Hall. ISBN 0-13-914101-4.
Rabiner & Gold 1975, p. 173 (Fig 3.75) Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, N.J.: Prentice-Hall. ISBN 0-13-914101-4.
Rabiner & Gold 1975, p. 175 Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, N.J.: Prentice-Hall. ISBN 0-13-914101-4.
Rabiner & Gold 1975, p. 59 (2.163) Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, N.J.: Prentice-Hall. ISBN 0-13-914101-4.

arxiv.org

Kak 2014. Kak, Subhash (2014). "Number theoretic Hilbert transform". Circuits, Systems and Signal Processing. 33 (8): 2539–2548. arXiv:1308.1688. doi:10.1007/s00034-014-9759-8. S2CID 21226699.

doi.org

Riesz 1928. Riesz, Marcel (1928). "Sur les fonctions conjuguées". Mathematische Zeitschrift (in French). 27 (1): 218–244. doi:10.1007/BF01171098. S2CID 123261514.
Calderón & Zygmund 1952. Calderón, A. P.; Zygmund, A. (1952). "On the existence of certain singular integrals". Acta Mathematica. 88 (1): 85–139. doi:10.1007/BF02392130.
This theorem is due to Riesz 1928, VII; see also Titchmarsh 1948, Theorem 101. Riesz, Marcel (1928). "Sur les fonctions conjuguées". Mathematische Zeitschrift (in French). 27 (1): 218–244. doi:10.1007/BF01171098. S2CID 123261514. Titchmarsh, E. (1986) [1948]. Introduction to the theory of Fourier integrals (2nd ed.). Oxford, UK: Clarendon Press. ISBN 978-0-8284-0324-5.
This result is due to Pichorides 1972; see also Grafakos 2004, Remark 4.1.8. Pichorides, S. (1972). "On the best value of the constants in the theorems of Riesz, Zygmund, and Kolmogorov". Studia Mathematica. 44 (2): 165–179. doi:10.4064/sm-44-2-165-179. Grafakos, Loukas (2004). Classical and Modern Fourier Analysis. Pearson Education. pp. 253–257. ISBN 0-13-035399-X.
Duistermaat & Kolk 2010, p. 211. Duistermaat, J. J.; Kolk, J. A. C. (2010). Distributions. Birkhäuser. doi:10.1007/978-0-8176-4675-2. ISBN 978-0-8176-4672-1.
See Bargmann 1947, Lang 1985, and Sugiura 1990. Bargmann, V. (1947). "Irreducible unitary representations of the Lorentz group". Ann. of Math. 48 (3): 568–640. doi:10.2307/1969129. JSTOR 1969129. Lang, Serge (1985). SL(2, $\mathbb {R}$ ). Graduate Texts in Mathematics. Vol. 105. New York, NY: Springer-Verlag. ISBN 0-387-96198-4. Sugiura, Mitsuo (1990). Unitary Representations and Harmonic Analysis: An Introduction. North-Holland Mathematical Library. Vol. 44 (2nd ed.). Elsevier. ISBN 0444885935.
Calderón & Zygmund 1952; see Fefferman 1971. Calderón, A. P.; Zygmund, A. (1952). "On the existence of certain singular integrals". Acta Mathematica. 88 (1): 85–139. doi:10.1007/BF02392130. Fefferman, C. (1971). "Characterizations of bounded mean oscillation". Bulletin of the American Mathematical Society. 77 (4): 587–588. doi:10.1090/S0002-9904-1971-12763-5. MR 0280994.
Fefferman 1971; Fefferman & Stein 1972 Fefferman, C. (1971). "Characterizations of bounded mean oscillation". Bulletin of the American Mathematical Society. 77 (4): 587–588. doi:10.1090/S0002-9904-1971-12763-5. MR 0280994. Fefferman, C.; Stein, E. M. (1972). "H^p spaces of several variables". Acta Mathematica. 129: 137–193. doi:10.1007/BF02392215. MR 0447953.
Kak 1970. Kak, Subhash (1970). "The discrete Hilbert transform". Proc. IEEE. 58 (4): 585–586. doi:10.1109/PROC.1970.7696.
Kak 2014. Kak, Subhash (2014). "Number theoretic Hilbert transform". Circuits, Systems and Signal Processing. 33 (8): 2539–2548. arXiv:1308.1688. doi:10.1007/s00034-014-9759-8. S2CID 21226699.

encyclopediaofmath.org

Bitsadze 2001. Bitsadze, A. V. (2001) [1994], "Boundary value problems of analytic function theory", Encyclopedia of Mathematics, EMS Press
Khvedelidze 2001. Khvedelidze, B. V. (2001) [1994], "Hilbert transform", Encyclopedia of Mathematics, EMS Press

fuchs-braun.com

Johansson, p. 24 Johansson, Mathias. "The Hilbert transform, Masters Thesis" (PDF). Archived from the original (PDF) on 2012-02-05.; also http://www.fuchs-braun.com/media/d9140c7b3d5004fbffff8007fffffff0.pdf Archived 2021-05-01 at the Wayback Machine
Johansson, p. 25 Johansson, Mathias. "The Hilbert transform, Masters Thesis" (PDF). Archived from the original (PDF) on 2012-02-05.; also http://www.fuchs-braun.com/media/d9140c7b3d5004fbffff8007fffffff0.pdf Archived 2021-05-01 at the Wayback Machine

jstor.org

See Bargmann 1947, Lang 1985, and Sugiura 1990. Bargmann, V. (1947). "Irreducible unitary representations of the Lorentz group". Ann. of Math. 48 (3): 568–640. doi:10.2307/1969129. JSTOR 1969129. Lang, Serge (1985). SL(2, $\mathbb {R}$ ). Graduate Texts in Mathematics. Vol. 105. New York, NY: Springer-Verlag. ISBN 0-387-96198-4. Sugiura, Mitsuo (1990). Unitary Representations and Harmonic Analysis: An Introduction. North-Holland Mathematical Library. Vol. 44 (2nd ed.). Elsevier. ISBN 0444885935.

mathworks.com

MathWorks. "hilbert – Discrete-time analytic signal using Hilbert transform". MATLAB Signal Processing Toolbox Documentation. Retrieved 2021-05-06.

rand.org

Bedrosian 1962. Bedrosian, E. (December 1962). A product theorem for Hilbert transforms (PDF) (Report). Rand Corporation. RM-3439-PR.

semanticscholar.org

api.semanticscholar.org

Riesz 1928. Riesz, Marcel (1928). "Sur les fonctions conjuguées". Mathematische Zeitschrift (in French). 27 (1): 218–244. doi:10.1007/BF01171098. S2CID 123261514.
This theorem is due to Riesz 1928, VII; see also Titchmarsh 1948, Theorem 101. Riesz, Marcel (1928). "Sur les fonctions conjuguées". Mathematische Zeitschrift (in French). 27 (1): 218–244. doi:10.1007/BF01171098. S2CID 123261514. Titchmarsh, E. (1986) [1948]. Introduction to the theory of Fourier integrals (2nd ed.). Oxford, UK: Clarendon Press. ISBN 978-0-8284-0324-5.
Kak 2014. Kak, Subhash (2014). "Number theoretic Hilbert transform". Circuits, Systems and Signal Processing. 33 (8): 2539–2548. arXiv:1308.1688. doi:10.1007/s00034-014-9759-8. S2CID 21226699.

stanford.edu

see.stanford.edu

Osgood, p. 320 Osgood, Brad, The Fourier Transform and its Applications (PDF), Stanford University, retrieved 2021-04-30
Osgood, p. 320 Osgood, Brad, The Fourier Transform and its Applications (PDF), Stanford University, retrieved 2021-04-30

ucsb.edu

web.ece.ucsb.edu

Isukapalli, p. 14 Isukapalli, Yogananda. "Types of linear phase FIR filters" (PDF). p. 18. Retrieved 2024-06-08.
Isukapalli, p. 18 Isukapalli, Yogananda. "Types of linear phase FIR filters" (PDF). p. 18. Retrieved 2024-06-08.
Isukapalli, p. 15 Isukapalli, Yogananda. "Types of linear phase FIR filters" (PDF). p. 18. Retrieved 2024-06-08.
Isukapalli, p. 18 Isukapalli, Yogananda. "Types of linear phase FIR filters" (PDF). p. 18. Retrieved 2024-06-08.

vxu.se

w3.msi.vxu.se

Johansson, p. 24 Johansson, Mathias. "The Hilbert transform, Masters Thesis" (PDF). Archived from the original (PDF) on 2012-02-05.; also http://www.fuchs-braun.com/media/d9140c7b3d5004fbffff8007fffffff0.pdf Archived 2021-05-01 at the Wayback Machine
Johansson, p. 25 Johansson, Mathias. "The Hilbert transform, Masters Thesis" (PDF). Archived from the original (PDF) on 2012-02-05.; also http://www.fuchs-braun.com/media/d9140c7b3d5004fbffff8007fffffff0.pdf Archived 2021-05-01 at the Wayback Machine

web.archive.org

Johansson, p. 24 Johansson, Mathias. "The Hilbert transform, Masters Thesis" (PDF). Archived from the original (PDF) on 2012-02-05.; also http://www.fuchs-braun.com/media/d9140c7b3d5004fbffff8007fffffff0.pdf Archived 2021-05-01 at the Wayback Machine
Johansson, p. 25 Johansson, Mathias. "The Hilbert transform, Masters Thesis" (PDF). Archived from the original (PDF) on 2012-02-05.; also http://www.fuchs-braun.com/media/d9140c7b3d5004fbffff8007fffffff0.pdf Archived 2021-05-01 at the Wayback Machine

wirelessinnovation.org

Carrick, Jaeger & harris 2011, p. 2 Carrick, Matt; Jaeger, Doug; harris, fred (2011). Design And Application Of A Hilbert Transformer In A Digital Receiver (PDF). Chantilly, VA: Proceedings of the SDR 11 Technical Conference and Product Exposition, Wireless Innovation Forum. Retrieved 2024-06-05.
Carrick, Jaeger & harris 2011, p. 3 Carrick, Matt; Jaeger, Doug; harris, fred (2011). Design And Application Of A Hilbert Transformer In A Digital Receiver (PDF). Chantilly, VA: Proceedings of the SDR 11 Technical Conference and Product Exposition, Wireless Innovation Forum. Retrieved 2024-06-05.
Carrick, Jaeger & harris 2011, p. 3 Carrick, Matt; Jaeger, Doug; harris, fred (2011). Design And Application Of A Hilbert Transformer In A Digital Receiver (PDF). Chantilly, VA: Proceedings of the SDR 11 Technical Conference and Product Exposition, Wireless Innovation Forum. Retrieved 2024-06-05.

worldcat.org

search.worldcat.org

Hilbert 1953. Hilbert, David (1953) [1912]. Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen [Framework for a General Theory of Linear Integral Equations] (in German). Leipzig & Berlin, DE (1912); New York, NY (1953): B.G. Teubner (1912); Chelsea Pub. Co. (1953). ISBN 978-3-322-00681-3. OCLC 988251080. Retrieved 2020-12-18 – via archive.org.{{cite book}}: CS1 maint: location (link)