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Hilbert transform
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== References == {{sfn whitelist |CITEREFBitsadze2001 |CITEREFKhvedelidze2001}} {{Refbegin}} * {{cite journal |last = Bargmann |first = V. |author-link=Valentine Bargmann |date = 1947 |title = Irreducible unitary representations of the Lorentz group |journal = Ann. of Math. |volume = 48 |issue = 3 |pages = 568–640 |doi = 10.2307/1969129 |jstor = 1969129 }} * {{cite report |last1 = Bedrosian |first1 = E. |date = December 1962 |title = A product theorem for Hilbert transforms |publisher = Rand Corporation |id = RM-3439-PR |url = http://www.rand.org/content/dam/rand/pubs/research_memoranda/2008/RM3439.pdf }} * {{springer |last = Bitsadze |first = A. V. |date = 2001 |title = Boundary value problems of analytic function theory |id = b/b017400 }} * {{cite book |last = Bracewell |first=R. |author-link=Ronald N. Bracewell |date = 2000 |title = The Fourier Transform and Its Applications |edition = 3rd |publisher = McGraw–Hill |isbn = 0-07-116043-4 }} * {{cite book |last = Brandwood |first = David |date = 2003 |title = Fourier Transforms in Radar and Signal Processing |publisher = Artech House |location = Boston |isbn = 9781580531740 }} * {{cite journal |last1 = Calderón |first1 = A. P. |author-link1 = Alberto Calderón |last2 = Zygmund |first2 = A. |author-link2 = Antoni Zygmund |date = 1952 |title = On the existence of certain singular integrals |journal = Acta Mathematica |volume = 88 |issue = 1 |pages = 85–139 |doi = 10.1007/BF02392130 |doi-access = free }} * {{cite conference |last1 = Carrick |first1 = Matt |last2 = Jaeger |first2 = Doug |last3 = harris |first3 = fred |title = Design And Application Of A Hilbert Transformer In A Digital Receiver |publisher = Proceedings of the SDR 11 Technical Conference and Product Exposition, Wireless Innovation Forum |date = 2011 |location = Chantilly, VA |url = https://www.wirelessinnovation.org/assets/Proceedings/2011/2011-1b-carrick.pdf |access-date = 2024-06-05 }} * {{cite book |last = Duoandikoetxea |first = J. |date = 2000 |title = Fourier Analysis |publisher = American Mathematical Society |isbn = 0-8218-2172-5 }} * {{cite book |last1 = Duistermaat |first1 = J. J. |author-link=Hans Duistermaat |last2 = Kolk |first2 = J. A. C. |date = 2010 |title = Distributions |publisher = Birkhäuser |isbn = 978-0-8176-4672-1 |doi = 10.1007/978-0-8176-4675-2 }} * {{cite book |last = Duren |first = P. |date = 1970 |title = Theory of H^p Spaces |publisher = Academic Press |place = New York, NY }} * {{cite journal |last = Fefferman |first = C. |author-link = Charles Fefferman |date = 1971 |title = Characterizations of bounded mean oscillation |journal = Bulletin of the American Mathematical Society |volume = 77 |issue = 4 |pages = 587–588 |mr = 0280994 |doi = 10.1090/S0002-9904-1971-12763-5 |doi-access = free |url = https://www.ams.org/bull/1971-77-04/S0002-9904-1971-12763-5/home.html }} * {{cite journal |last1 = Fefferman |first1 = C. |last2 = Stein |first2 = E. M. |date = 1972 |title = H^p spaces of several variables |journal = Acta Mathematica |volume = 129 |pages = 137–193 |mr = 0447953 |doi = 10.1007/BF02392215 |doi-access = free }} * {{cite book |last =Franks |first =L.E. |title =Signal Theory |editor=Thomas Kailath |publisher =Prentice Hall |series =Information theory |date =September 1969 |location =Englewood Cliffs, NJ |isbn =0138100772 }} * {{cite book |last1 = Gel'fand |first1 = I. M. |author-link1 = Israel Gelfand |last2 = Shilov |first2 = G. E. |date = 1968 |title = Generalized Functions |volume = 2 |pages = 153–154 |publisher = Academic Press |isbn = 0-12-279502-4 }} * {{cite book |last = Grafakos |first = Loukas |date = 2004 |title = Classical and Modern Fourier Analysis |pages = 253–257 |publisher = Pearson Education |isbn = 0-13-035399-X }} * {{cite book |last1 = Hardy |first1 = G. H. |author-link1 = G. H. Hardy |last2 = Littlewood |first2 = J. E. |author-link2 = J. E. Littlewood |last3 = Pólya |first3 = G. |author-link3 = G. Pólya |date = 1952 |title = Inequalities |publisher = Cambridge University Press |place = Cambridge, UK |isbn = 0-521-35880-9 }} * {{cite book |last = Hilbert |first = David |author-link = David Hilbert |date = 1953 |orig-year = 1912 |title = Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen |trans-title = Framework for a General Theory of Linear Integral Equations |language = de |place = Leipzig & Berlin, DE (1912); New York, NY (1953) |publisher = B.G. Teubner (1912); Chelsea Pub. Co. (1953) |isbn = 978-3-322-00681-3 |oclc = 988251080 |url = https://archive.org/details/grundzugeallg00hilbrich/page/n7 |via = archive.org |access-date = 2020-12-18 }} * {{cite web | last = Isukapalli | first = Yogananda | title = Types of linear phase FIR filters | url = https://web.ece.ucsb.edu/~yoga/courses/DSP/P10_Linear_phase_FIR.pdf | page = 18 | access-date = 2024-06-08 }} * {{cite web |last = Johansson |first = Mathias |title = The Hilbert transform, Masters Thesis |url = http://w3.msi.vxu.se/exarb/mj_ex.pdf |archive-url = https://web.archive.org/web/20120205214945/http://w3.msi.vxu.se/exarb/mj_ex.pdf |archive-date = 2012-02-05 }}; also http://www.fuchs-braun.com/media/d9140c7b3d5004fbffff8007fffffff0.pdf {{Webarchive|url=https://web.archive.org/web/20210501230529/http://www.fuchs-braun.com/media/d9140c7b3d5004fbffff8007fffffff0.pdf |date=2021-05-01 }} * {{cite journal |last = Kak |first = Subhash |author-link = Subhash Kak |date = 1970 |title = The discrete Hilbert transform |journal = Proc. IEEE |volume = 58 |issue = 4 |pages = 585–586 |doi = 10.1109/PROC.1970.7696 }} * {{cite journal |last = Kak |first = Subhash |author-link = Subhash Kak |date = 2014 |title = Number theoretic Hilbert transform |journal = Circuits, Systems and Signal Processing |volume = 33 |issue = 8 |pages = 2539–2548 |doi = 10.1007/s00034-014-9759-8 |arxiv = 1308.1688 |s2cid = 21226699 }} * {{springer |last = Khvedelidze |first = B. V. |date = 2001 |title = Hilbert transform |id = H/h047430 }} * {{cite book |last = King |first = Frederick W. |date = 2009a |title = Hilbert Transforms |volume = 1 |publisher = Cambridge University Press |place = Cambridge, UK }} * {{cite book |last = King |first = Frederick W. |date = 2009b |title = Hilbert Transforms |volume = 2 |pages = 453 |publisher = Cambridge University Press |place = Cambridge, UK |isbn = 978-0-521-51720-1 }} * {{cite book |last = Kress |first = Rainer |date = 1989 |title = Linear Integral Equations |page = 91 |publisher = Springer-Verlag |place = New York, NY |isbn = 3-540-50616-0 }} * {{cite book |last = Lang |first = Serge |author-link = Serge Lang |date = 1985 |title = SL(2,<math>\mathbb{R}</math>) |series = Graduate Texts in Mathematics |volume = 105 |publisher = Springer-Verlag |place = New York, NY |isbn = 0-387-96198-4 }} * {{Cite book |last1=Oppenheim |first1=Alan V. |author-link=Alan V. Oppenheim |last2=Schafer |first2=Ronald W. |author2-link=Ronald W. Schafer |last3=Buck |first3=John R. |title=Discrete-time signal processing |year=1999 |publisher=Prentice Hall |location=Upper Saddle River, N.J. |isbn=0-13-754920-2 |edition=2nd |chapter=11.4.1 |url-access=registration |url=https://archive.org/details/discretetimesign00alan |quote=The exactness of the phase of type III and IV FIR systems is a compelling motivation for their use in approximating Hilbert transformers. }} * {{Citation | last =Osgood | first =Brad | title =The Fourier Transform and its Applications | publisher =Stanford University | date = | year = | url =https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf | access-date =2021-04-30 }} * {{cite book |last = Pandey |first = J. N. |date = 1996 |title = The Hilbert transform of Schwartz distributions and applications |publisher = Wiley-Interscience |isbn = 0-471-03373-1 }} * {{cite journal |last = Pichorides |first = S. |author-link=Stylianos Pichorides |date = 1972 |title = On the best value of the constants in the theorems of Riesz, Zygmund, and Kolmogorov |journal = Studia Mathematica |volume = 44 |issue = 2 |pages = 165–179 |doi = 10.4064/sm-44-2-165-179 |doi-access = free }} * {{Cite book | last1=Rabiner|first1=Lawrence R. | last2=Gold|first2=Bernard | title=Theory and application of digital signal processing | year=1975 | publisher=Prentice-Hall | location=Englewood Cliffs, N.J. | isbn=0-13-914101-4 | url=https://archive.org/details/theoryapplicatio00rabi }} * {{cite journal |last = Riesz |first = Marcel |author-link = Marcel Riesz |title = Sur les fonctions conjuguées |date = 1928 |journal = Mathematische Zeitschrift |volume = 27 |issue = 1 |pages = 218–244 |doi = 10.1007/BF01171098 |s2cid = 123261514 |language = fr }} * {{cite book |last1 = Rosenblum |first1 = Marvin |last2 = Rovnyak |first2 = James |date = 1997 |title = Hardy classes and operator theory |publisher = Dover |isbn = 0-486-69536-0 }} * {{cite book |last = Schwartz |first = Laurent |author-link = Laurent Schwartz |date = 1950 |title = Théorie des distributions |publisher = Hermann |place = Paris, FR }} * {{cite book |last1 = Schreier |first1 = P. |last2 = Scharf |first2 = L. |date = 2010 |title = Statistical signal processing of complex-valued data: The theory of improper and noncircular signals |publisher = Cambridge University Press |place = Cambridge, UK }} * {{cite web |last = Smith |first = J. O. |date = 2007 |title = Analytic Signals and Hilbert Transform Filters, in Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications |edition = 2nd |access-date = 2021-04-29 |url = https://ccrma.stanford.edu/~jos/r320/Analytic_Signals_Hilbert_Transform.html }}; also https://www.dsprelated.com/freebooks/mdft/Analytic_Signals_Hilbert_Transform.html * {{cite book |last = Stein |first = Elias |author-link = Elias Stein |date = 1970 |title = Singular integrals and differentiability properties of functions |publisher = Princeton University Press |isbn = 0-691-08079-8 |url = https://archive.org/details/singularintegral0000stei |url-access = registration }} * {{cite book |last1 = Stein |first1 = Elias |author-link1 = Elias Stein |last2 = Weiss |first2 = Guido |date = 1971 |title = Introduction to Fourier Analysis on Euclidean Spaces |publisher = Princeton University Press |isbn = 0-691-08078-X |url = https://archive.org/details/introductiontofo0000stei |url-access = registration }} * {{cite book |last = Sugiura |first = Mitsuo |date = 1990 |title = Unitary Representations and Harmonic Analysis: An Introduction |edition = 2nd |series = North-Holland Mathematical Library |volume = 44 |publisher = Elsevier |isbn = 0444885935 }} * {{cite book |last = Titchmarsh |first = E. |author-link = Edward Charles Titchmarsh |orig-year = 1948 |date = 1986 |title = Introduction to the theory of Fourier integrals |edition = 2nd |isbn = 978-0-8284-0324-5 |publisher = Clarendon Press |place = Oxford, UK |ref = {{sfnRef|Titchmarsh|1948}} }} * {{cite book |last=Tretter |first=Steven A. |title=Communication System Design Using DSP Algorithms |editor=R.W.Lucky |publisher=Springer |date=1995 |location=New York |isbn=0306450321 }} * {{cite book |last = Zygmund |first = Antoni |author-link = Antoni Zygmund |orig-year = 1968 |date = 1988 |title = Trigonometric Series |edition = 2nd <!-- |title-link= Trigonometric Series -- link is to article on the same subject, but it is not a reference for the book with the same title --> |publisher = Cambridge University Press |place = Cambridge, UK |isbn = 978-0-521-35885-9 |ref = {{sfnRef|Zygmund|1968}} }} {{Refend}}
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