Fourier dönüşümü: Revizyonlar arasındaki fark
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*[[Dönüşüm(matematik)]] |
*[[Dönüşüm(matematik)]] |
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==Kaynakça== |
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*{{Citation |editor-last=Boashash|editor-first=B.|title=Time-Frequency Signal Analysis and Processing: A Comprehensive Reference|publisher=Elsevier Science|publication-place= Oxford|year=2003 |isbn=0-08-044335-4}} |
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*{{Citation | author =[[Salomon Bochner|Bochner S.]], [[K. S. Chandrasekharan|Chandrasekharan K.]] | title=Fourier Transforms | publisher= Princeton University Press | year=1949}} |
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* {{citation|first=R. N.|last=Bracewell|title=The Fourier Transform and Its Applications|edition=3rd|publication-place=Boston|publisher=McGraw-Hill|year=2000|isbn=0-07-116043-4}}. |
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* {{citation|first1=George|last1=Campbell|first2=Ronald|last2=Foster|title=Fourier Integrals for Practical Applications|publication-place=New York|publisher=D. Van Nostrand Company, Inc.|year=1948}}. |
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*{{citation| first=E. U.| last=[[Edward Condon|Condon]] | title=Immersion of the Fourier transform in a continuous group of functional transformations| journal=Proc. Nat. Acad. Sci. USA |
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|volume= 23| pages= 158–164 | year=1937 }}. |
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* {{citation|last=Duoandikoetxea|first=Javier|title=Fourier Analysis|publisher=American Mathematical Society|year=2001|isbn=0-8218-2172-5}}. |
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* {{citation|last1=Dym|first1=H|first2=H|last2=McKean|authorlink1=Harry Dym|title=Fourier Series and Integrals|publisher=Academic Press|year=1985|isbn=978-0-12-226451-1}}. |
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* {{citation|editor-last=Erdélyi|editor-first=Arthur|title=Tables of Integral Transforms|volume=1|publication-place=New Your|publisher=McGraw-Hill|year=1954}} |
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* {{citation|last=Fourier|first=J. B. Joseph|authorlink=Joseph_Fourier|title=Théorie Analytique de la Chaleur|publication-place=Paris|url=http://books.google.com/books?id=TDQJAAAAIAAJ&pg=PA525&dq=%22c%27est-%C3%A0-dire+qu%27on+a+l%27%C3%A9quation%22&hl=en&sa=X&ei=SrC7T9yKBorYiALVnc2oDg&sqi=2&ved=0CEAQ6AEwAg#v=onepage&q=%22c%27est-%C3%A0-dire%20qu%27on%20a%20l%27%C3%A9quation%22&f=false|publisher=Chez Firmin Didot, père et fils|year=1822}} |
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* {{citation|last1=Fourier|first1=J. B. Joseph |title=The Analytical Theory of Heat |url=http://books.google.com/books?id=-N8EAAAAYAAJ&pg=PA408&dq=%22that+is+to+say,+that+we+have+the+equation%22&hl=en&sa=X&ei=F667T-u5I4WeiALEwpHXDQ&ved=0CDgQ6AEwAA#v=onepage&q=%22that%20is%20to%20say%2C%20that%20we%20have%20the%20equation%22&f=false |first2=Alexander, translator |last2=Freeman |year=1878 |publisher=The University Press}} |
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* {{citation|first=Loukas|last=Grafakos|title=Classical and Modern Fourier Analysis|publisher=Prentice-Hall|year=2004|isbn=0-13-035399-X}}. |
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* {{citation|first=Loukas|last=Grafakos|first2=Gerald|last2=Teschl|authorlink2=Gerald Teschl|title=On Fourier transforms of radial functions and distributions|journal=J. Fourier Anal. Appl.|volume=19|pages=167–179|year=2013|doi=10.1007/s00041-012-9242-5}}. |
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* {{Citation | last1=Hewitt | first1=Edwin | last2=Ross | first2=Kenneth A. | title=Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups | publisher=Springer-Verlag | location=Berlin, New York | series=Die Grundlehren der mathematischen Wissenschaften, Band 152 | mr=0262773 | year=1970}}. |
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* {{citation|first=L.|last=Hörmander|authorlink=Lars Hörmander|title=Linear Partial Differential Operators, Volume 1|publisher=Springer-Verlag|year=1976|isbn=978-3-540-00662-6}}. |
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* {{citation|first = J.F.|last = James|title=A Student's Guide to Fourier Transforms|edition=3rd|publication-place=New York|publisher=Cambridge University Press|year=2011|isbn=978-0-521-17683-5}}. |
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* {{citation|first=Gerald|last=Kaiser|title=A Friendly Guide to Wavelets|year=1994|publisher=Birkhäuser|isbn=0-8176-3711-7 |url=http://books.google.com/books?id=rfRnrhJwoloC&pg=PA29&dq=%22becomes+the+Fourier+%28integral%29+transform%22&hl=en&sa=X&ei=osO7T7eFOqqliQK3goXoDQ&ved=0CDQQ6AEwAA#v=onepage&q=%22becomes%20the%20Fourier%20%28integral%29%20transform%22&f=false}} |
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* {{citation|first=David|last=Kammler|title=A First Course in Fourier Analysis|year=2000|publisher=Prentice Hall|isbn=0-13-578782-3}} |
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* {{citation|first=Yitzhak|last=Katznelson|title=An introduction to Harmonic Analysis|year=1976|publisher=Dover|isbn=0-486-63331-4}} |
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* {{Citation | last1=Knapp | first1=Anthony W. | title=Representation Theory of Semisimple Groups: An Overview Based on Examples | url=http://books.google.com/?id=QCcW1h835pwC | publisher=[[Princeton University Press]] | isbn=978-0-691-09089-4 | year=2001}} |
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* {{citation|first=Mark|last=Pinsky|title=Introduction to Fourier Analysis and Wavelets|year=2002|publisher=Brooks/Cole|isbn=0-534-37660-6 |url=http://books.google.com/books?id=tlLE4KUkk1gC&pg=PA256&dq=%22The+Fourier+transform+of+the+measure%22&hl=en&sa=X&ei=w8e7T43XJsiPiAKZztnRDQ&ved=0CEUQ6AEwAg#v=onepage&q=%22The%20Fourier%20transform%20of%20the%20measure%22&f=false}} |
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* {{citation|first1=A. D.|last1=Polyanin|first2=A. V.|last2=Manzhirov|title=Handbook of Integral Equations|publisher=CRC Press|publication-place=Boca Raton|year=1998|isbn=0-8493-2876-4}}. |
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* {{citation|first=Walter|last=Rudin|title=Real and Complex Analysis|publisher=McGraw Hill| edition=Third|year=1987|isbn=0-07-100276-6|location=Singapore }}. |
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*{{citation |first=Matiur |last=Rahman |url=http://books.google.com/books?id=k_rdcKaUdr4C&pg=PA10 |isbn=1845645642 |publisher=WIT Press |title=Applications of Fourier Transforms to Generalized Functions |year=2011}}. |
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* {{citation |last1=Stein|first1=Elias|first2=Rami|last2=Shakarchi|title=Fourier Analysis: An introduction|publisher=Princeton University Press|year=2003|isbn=0-691-11384-X|url=http://books.google.com/books?id=FAOc24bTfGkC&pg=PA158&dq=%22The+mathematical+thrust+of+the+principle%22&hl=en&sa=X&ei=Esa7T5PZIsqriQKluNjPDQ&ved=0CDQQ6AEwAA#v=onepage&q=%22The%20mathematical%20thrust%20of%20the%20principle%22&f=false}}. |
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* {{citation|last1=Stein|first1=Elias|authorlink1=Elias Stein|first2=Guido|last2=Weiss|authorlink2=Guido Weiss|title=Introduction to Fourier Analysis on Euclidean Spaces|publisher=Princeton University Press|year=1971|isbn=978-0-691-08078-9|location=Princeton, N.J. |url=http://books.google.com/books?id=YUCV678MNAIC&dq=editions:xbArf-TFDSEC&source=gbs_navlinks_s}}. |
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* {{citation|last=Taneja|first=HC |title=Advanced Engineering Mathematics:, Volume 2 |url=http://books.google.com/books?id=X-RFRHxMzvYC&pg=PA192&dq=%22The+Fourier+integral+can+be+regarded+as+an+extension+of+the+concept+of+Fourier+series%22&hl=en&sa=X&ei=D4rDT_vdCueQiAKF6PWeCA&ved=0CDQQ6AEwAA#v=onepage&q=%22The%20Fourier%20integral%20can%20be%20regarded%20as%20an%20extension%20of%20the%20concept%20of%20Fourier%20series%22&f=false |chapter=Chapter 18: Fourier integrals and Fourier transforms |isbn=8189866567|year=2008 |publisher=I. K. International Pvt Ltd |publication-place=New Delhi, India}}. |
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* {{citation|last=Titchmarsh|first=E|authorlink=Edward Charles Titchmarsh|title=Introduction to the theory of Fourier integrals|isbn=978-0-8284-0324-5|year=1948|edition=2nd|publication-date=1986|publisher=Clarendon Press|publication-place=Oxford University}}. |
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* {{citation|first=R. G.|last=Wilson|title=Fourier Series and Optical Transform Techniques in Contemporary Optics|publisher=Wiley|year=1995|isbn=0-471-30357-7|location=New York}}. |
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* {{citation|first=K.|last=Yosida|authorlink=Kōsaku Yosida|title=Functional Analysis|publisher=Springer-Verlag|year=1968|isbn=3-540-58654-7}}. |
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==Dış bağlantılar== |
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* [http://www.nbtwiki.net/doku.php?id=tutorial:the_discrete_fourier_transformation_dft The Discrete Fourier Transformation (DFT): Definition and numerical examples] — A Matlab tutorial |
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* [http://www.thefouriertransform.com The Fourier Transform Tutorial Site] (thefouriertransform.com) |
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* [http://www.westga.edu/~jhasbun/osp/Fourier.htm Fourier Series Applet] (Tip: drag magnitude or phase dots up or down to change the wave form). |
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* [http://www.dspdimension.com/fftlab/ Stephan Bernsee's FFTlab] (Java Applet) |
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* [http://www.academicearth.org/courses/the-fourier-transform-and-its-applications Stanford Video Course on the Fourier Transform] |
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*{{springer|title=Fourier transform|id=p/f041150}} |
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* {{MathWorld | urlname= FourierTransform | title= Fourier Transform}} |
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* [http://www.dspdimension.com/admin/dft-a-pied/ The DFT “à Pied”: Mastering The Fourier Transform in One Day] at The DSP Dimension |
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* [http://www.fourier-series.com/f-transform/index.html An Interactive Flash Tutorial for the Fourier Transform] |
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*[http://www.patternizando.com.br/2013/05/transformadas-discretas-wavelet-e-fourier-em-java/ Java Library for DFT] |
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*[http://talkera.org.cp-in-1.webhostbox.net/wp/?p=89 FFT in Python] |
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*[http://www.civilized.com/files/newfourier.pdf Fourier Transforms] Gary D. Knott |
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*[http://www.continuummechanics.org/cm/fourierxforms.html Fourier Transforms] on [http://www.continuummechanics.org/ www.continuummechanics.org] |
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{{DEFAULTSORT:Fourier Transform}} |
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[[Category:Concepts in physics]] |
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[[Category:Fourier analysis]] |
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[[Category:Integral transforms]] |
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[[Category:Unitary operators]] |
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[[Category:Joseph Fourier]] |
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[[Category:Mathematical physics]] |
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[[Category:Theoretical physics]] |
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[[Kategori:Fourier dönüşümü| ]] |
[[Kategori:Fourier dönüşümü| ]] |
Sayfanın 22.46, 17 Haziran 2014 tarihindeki hâli
Fourier dönüşümü, sürekli ve ayrık olarak ikiye ayrılabilir. İki dönüşüm de bir nesneyi ortogonal iki uzay arasında eşler. Sürekli nesneler için dönüşüm:
ve
şeklinde verilir. Yukarıdaki dönüşümde görüleceği üzere x uzayındaki bir nesne k uzayında tanımlanmıştır. Bu dönüşüm diferansiyel denklemlerin çözümünde çok büyük rahatlık sağlar zira bu dönüşüm sayesinde x uzayındaki diferansiyel denklemler k uzayında lineer denklemler olarak ifade edilirler. K uzayında bu denklemin çözümü bulunduktan sonra ters dönüşümle x uzayındaki karşılığı elde edilir, ki bu diferansiyel denklemin çözümüdür. Birinci dönüşümdeki ifade ikinci dönüşümde yerine oturtularak,
,
ifadesine ulaşılır. Parantez içindeki ifadenin olduğu görülebilir. Anlaşıldığı üzere eşlemesine Fourier Dönüşümü, eşlemesine de Ters Fourier Dönüşümü denir ve bu eşlemeler (mapping) yapılırken baş harfleri büyük yazılarak gösterilir (FD ve TFD). Parantez içindeki ifadenin Delta fonksiyonunun temsili olması ise açıkça bir düz ve bir ters Fourier dönüşümü yapılan bir ifadenin kendine eşit olmasından kaynaklanır. Dönüşüm uzayları keyfi seçilebilir ancak fizikte, konum uzayından momentum uzayına ve zaman uzayından enerji uzayına De Broglie-Einstein denklemleriyle geçişler tanımlanmıştır.
Ayrıca bakınız
- Analog işaret işleme
- Beevers–Lipson şeridi
- Ayrık Fourier dönüşümü
- Ayrık-zaman Fourier dönüşümü
- Hızlı Fourier dönüşümü
- Fourier integral işlemci
- Fourier ters teoremi
- Fourier çarpıcı
- Fourier serisi
- Fourier sin dönüşümü
- Fourier–Deligne dönüşümü
- Fourier–Mukai dönüşümü
- Kesirli Fourier dönüşümü
- Indirek Fourier dönüşümü
- Integral dönüşüm
- Laplace dönüşümü
- Doğrusal kurallı dönüşüm
- Mellin dönüşümü
- Çokboyutlu dönüşüm
- NGC 4622,NGC 4622 Fourier dönüşümü özellikle görüntü m = 2.
- Kısa-zaman Fourier dönüşümü
- Uzay-zaman Fourier dönüşümü
- Spektral kestirim
- Sembolik integrasyon
- Zaman esneme dağılımlı Fourier dönüşümü
- Dönüşüm(matematik)
Kaynakça
- Boashash, B., (Ed.) (2003), Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Oxford: Elsevier Science, ISBN 0-08-044335-4
- Bochner S., Chandrasekharan K. (1949), Fourier Transforms, Princeton University Press
- Bracewell, R. N. (2000), The Fourier Transform and Its Applications (3rd bas.), Boston: McGraw-Hill, ISBN 0-07-116043-4.
- Campbell, George; Foster, Ronald (1948), Fourier Integrals for Practical Applications, New York: D. Van Nostrand Company, Inc..
- Condon, E. U. (1937), "Immersion of the Fourier transform in a continuous group of functional transformations", Proc. Nat. Acad. Sci. USA, 23, ss. 158–164.
- Duoandikoetxea, Javier (2001), Fourier Analysis, American Mathematical Society, ISBN 0-8218-2172-5.
- Dym, H; McKean, H (1985), Fourier Series and Integrals, Academic Press, ISBN 978-0-12-226451-1.
- Erdélyi, Arthur, (Ed.) (1954), Tables of Integral Transforms, 1, New Your: McGraw-Hill
- Fourier, J. B. Joseph (1822), Théorie Analytique de la Chaleur, Paris: Chez Firmin Didot, père et fils
- Fourier, J. B. Joseph; Freeman, Alexander, translator (1878), The Analytical Theory of Heat, The University Press
- Grafakos, Loukas (2004), Classical and Modern Fourier Analysis, Prentice-Hall, ISBN 0-13-035399-X.
- Grafakos, Loukas; Teschl, Gerald (2013), "On Fourier transforms of radial functions and distributions", J. Fourier Anal. Appl., 19, ss. 167–179, doi:10.1007/s00041-012-9242-5.
- Hewitt, Edwin; Ross, Kenneth A. (1970), Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Berlin, New York: Springer-Verlag, MR 0262773.
- Hörmander, L. (1976), Linear Partial Differential Operators, Volume 1, Springer-Verlag, ISBN 978-3-540-00662-6.
- James, J.F. (2011), A Student's Guide to Fourier Transforms (3rd bas.), New York: Cambridge University Press, ISBN 978-0-521-17683-5.
- Kaiser, Gerald (1994), A Friendly Guide to Wavelets, Birkhäuser, ISBN 0-8176-3711-7
- Kammler, David (2000), A First Course in Fourier Analysis, Prentice Hall, ISBN 0-13-578782-3
- Katznelson, Yitzhak (1976), An introduction to Harmonic Analysis, Dover, ISBN 0-486-63331-4
- Knapp, Anthony W. (2001), Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton University Press, ISBN 978-0-691-09089-4
- Pinsky, Mark (2002), Introduction to Fourier Analysis and Wavelets, Brooks/Cole, ISBN 0-534-37660-6
- Polyanin, A. D.; Manzhirov, A. V. (1998), Handbook of Integral Equations, Boca Raton: CRC Press, ISBN 0-8493-2876-4.
- Rudin, Walter (1987), Real and Complex Analysis (Third bas.), Singapore: McGraw Hill, ISBN 0-07-100276-6.
- Rahman, Matiur (2011), Applications of Fourier Transforms to Generalized Functions, WIT Press, ISBN 1845645642.
- Stein, Elias; Shakarchi, Rami (2003), Fourier Analysis: An introduction, Princeton University Press, ISBN 0-691-11384-X.
- Stein, Elias; Weiss, Guido (1971), Introduction to Fourier Analysis on Euclidean Spaces, Princeton, N.J.: Princeton University Press, ISBN 978-0-691-08078-9.
- Taneja, HC (2008), "Chapter 18: Fourier integrals and Fourier transforms", Advanced Engineering Mathematics:, Volume 2, New Delhi, India: I. K. International Pvt Ltd, ISBN 8189866567.
- Titchmarsh, E (1948), Introduction to the theory of Fourier integrals (2nd bas.), Oxford University: Clarendon Press (1986 tarihinde yayınlandı), ISBN 978-0-8284-0324-5.
- Wilson, R. G. (1995), Fourier Series and Optical Transform Techniques in Contemporary Optics, New York: Wiley, ISBN 0-471-30357-7.
- Yosida, K. (1968), Functional Analysis, Springer-Verlag, ISBN 3-540-58654-7.
Dış bağlantılar
- The Discrete Fourier Transformation (DFT): Definition and numerical examples — A Matlab tutorial
- The Fourier Transform Tutorial Site (thefouriertransform.com)
- Fourier Series Applet (Tip: drag magnitude or phase dots up or down to change the wave form).
- Stephan Bernsee's FFTlab (Java Applet)
- Stanford Video Course on the Fourier Transform
- Hazewinkel, Michiel, (Ed.) (2001), "Fourier transform", Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104
- Eric W. Weisstein, Fourier Transform (MathWorld)
- The DFT “à Pied”: Mastering The Fourier Transform in One Day at The DSP Dimension
- An Interactive Flash Tutorial for the Fourier Transform
- Java Library for DFT
- FFT in Python
- Fourier Transforms Gary D. Knott
- Fourier Transforms on www.continuummechanics.org
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