تحويل فورييه السريع: الفرق بين النسختين
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سطر 53:
* [[سلسلة زمنية]]
==مراجع==== References ==
<references />
* {{cite journal
|first1=N.
|last1=Brenner
|first2=C.
|last2=Rader
|year=1976
|title= A New Principle for Fast Fourier Transformation
|journal=IEEE Acoustics, Speech & Signal Processing
|volume=24
|issue=3
|doi=10.1109/TASSP.1976.1162805
|pages=264–266
}}
* {{Cite document|first=E. O.|last=Brigham|title=The Fast Fourier Transform|publication-place=New York|publisher=Prentice-Hall|year=2002|postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}
* [[Thomas H. Cormen]], [[Charles E. Leiserson]], [[Ronald L. Rivest]], and [[Clifford Stein]], 2001. ''[[Introduction to Algorithms]]'', 2nd. ed. MIT Press and McGraw-Hill. ISBN 0-262-03293-7. Especially chapter 30, "Polynomials and the FFT."
* {{cite journal
|first1=Pierre
|last1=Duhamel
|year=1990
|doi=10.1109/29.60070
|title=Algorithms meeting the lower bounds on the multiplicative complexity of length-<math>2^n</math> DFTs and their connection with practical algorithms
|journal=IEEE Trans. Acoust. Speech. Sig. Proc.
|volume=38
|issue=9
|pages=1504–151
}}
* P. Duhamel and M. Vetterli, 1990, {{doi-inline|10.1016/0165-1684(90)90158-U|Fast Fourier transforms: a tutorial review and a state of the art}}, ''Signal Processing'' '''19''': 259–299.
* A. Edelman, P. McCorquodale, and S. Toledo, 1999, {{doi-inline|10.1137/S1064827597316266|The Future Fast Fourier Transform?}}, ''SIAM J. Sci. Computing'' '''20''': 1094–1114.
* D. F. Elliott, & K. R. Rao, 1982, ''Fast transforms: Algorithms, analyses, applications''. New York: Academic Press.
* Funda Ergün, 1995, {{doi-inline|10.1145/225058.225167|Testing multivariate linear functions: Overcoming the generator bottleneck}}, ''Proc. 27th ACM Symposium on the Theory of Computing'': 407–416.
*M. Frigo and S. G. Johnson, 2005, "[http://fftw.org/fftw-paper-ieee.pdf The Design and Implementation of FFTW3]," ''Proceedings of the IEEE'' '''93''': 216–231.
* [[Carl Friedrich Gauss]], 1866. "[http://lseet.univ-tln.fr/~iaroslav/Gauss_Theoria_interpolationis_methodo_nova_tractata.php Theoria interpolationis methodo nova tractata]," ''Werke'' band '''3''', 265–327. Göttingen: Königliche Gesellschaft der Wissenschaften.
* W. M. Gentleman and G. Sande, 1966, "Fast Fourier transforms—for fun and profit," ''Proc. AFIPS'' '''29''': 563–578. {{doi|10.1145/1464291.1464352}}
* H. Guo and C. S. Burrus, 1996, {{doi-inline|10.1117/12.255236|Fast approximate Fourier transform via wavelets transform}}, ''Proc. SPIE Intl. Soc. Opt. Eng.'' '''2825''': 250–259.
* H. Guo, G. A. Sitton, C. S. Burrus, 1994, {{doi-inline|10.1109/ICASSP.1994.389994|The Quick Discrete Fourier Transform}}, ''Proc. IEEE Conf. Acoust. Speech and Sig. Processing (ICASSP)'' '''3''': 445–448.
* Steve Haynal and Heidi Haynal, "[http://jsat.ewi.tudelft.nl/content/volume7/JSAT7_13_Haynal.pdf Generating and Searching Families of FFT Algorithms]", ''Journal on Satisfiability, Boolean Modeling and Computation'' vol. 7, pp. 145–187 (2011).
* {{cite journal
|last1=Heideman
|first1=M. T.
|first2=D. H.
|last2=Johnson
|first3=C. S.
|last3=Burrus
|doi=10.1109/MASSP.1984.1162257
|title=Gauss and the history of the fast Fourier transform
|journal=IEEE ASSP Magazine
|volume=1
|issue=4
|pages=14–21
|year=1984
}}
* {{cite journal
|first1=Michael T.
|last1=Heideman
|first2=C. Sidney
|last2=Burrus
|year=1986
|doi=10.1109/TASSP.1986.1164785
|title=On the number of multiplications necessary to compute a length-<math>2^n</math> DFT
|journal=IEEE Trans. Acoust. Speech. Sig. Proc.
|volume=34
|issue=1
|pages=91–95
}}
* S. G. Johnson and M. Frigo, 2007. "[http://www.fftw.org/newsplit.pdf A modified split-radix FFT with fewer arithmetic operations]," ''IEEE Trans. Signal Processing'' '''55''' (1): 111–119.
* T. Lundy and J. Van Buskirk, 2007. "A new matrix approach to real FFTs and convolutions of length 2<sup>k</sup>," ''Computing'' '''80''' (1): 23-45.
*Kent, Ray D. and Read, Charles (2002). ''Acoustic Analysis of Speech''. ISBN 0-7693-0112-6. Cites Strang, G. (1994)/May–June). Wavelets. ''American Scientist, 82,'' 250-255.
* {{cite journal
|first1=Jacques
|last1=Morgenstern
|year=1973
|doi=10.1145/321752.321761
|title=Note on a lower bound of the linear complexity of the fast Fourier transform
|journal=J. ACM
|volume=20
|issue=2
|pages=305–306
}}
* {{cite journal
|doi=10.1007/BF01261607
|first1=M. J.
|last1=Mohlenkamp
|year=1999
|title=A fast transform for spherical harmonics
|journal=J. Fourier Anal. Appl.
|volume=5
|issue=2-3
|pages=159–184
|url=http://www.math.ohiou.edu/~mjm/research/MOHLEN1999P.pdf
}}
* {{cite journal
|first1=H. J.
|last1=Nussbaumer
|year=1977
|doi=10.1049/el:19770280
|title=Digital filtering using polynomial transforms
|journal=Electronics Lett.
|volume=13
|issue=13
|pages=386–387
}}
* V. Pan, 1986, {{doi-inline|10.1016/0020-0190(86)90035-9|The trade-off between the additive complexity and the asyncronicity of linear and bilinear algorithms}}, ''Information Proc. Lett.'' '''22''': 11-14.
* Christos H. Papadimitriou, 1979, {{doi-inline|10.1145/322108.322118|Optimality of the fast Fourier transform}}, ''J. ACM'' '''26''': 95-102.
* D. Potts, G. Steidl, and M. Tasche, 2001. "[http://www.tu-chemnitz.de/~potts/paper/ndft.pdf Fast Fourier transforms for nonequispaced data: A tutorial]", in: J.J. Benedetto and P. Ferreira (Eds.), ''Modern Sampling Theory: Mathematics and Applications'' (Birkhauser).
==وصلات خارجية==
* [http://www.cs.pitt.edu/~kirk/cs1501/animations/FFT.html Fast Fourier Algorithm]
* ''[http://cnx.org/content/col10550/ Fast Fourier Transforms]'', [[Connexions]] online book edited by C. Sidney Burrus, with chapters by C. Sidney Burrus, Ivan Selesnick, Markus Pueschel, Matteo Frigo, and Steven G. Johnson (2008).
* [http://www.fftw.org/links.html Links to FFT code and information online.]
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