[See also books on numerical analysis, for example 14975 Naldi/, 16027 Naldi/, 1002 Stoer, 15811 Quarteroni/ 2.] -------------------------------------------------------------------------- 580 Dietmar Achilles: Die Fouriertransformation in der Signalverarbeitung. Springer 1985. 24431 Patrick Arenz: Diskrete und schnelle Fouriertransformation. Internet 2005, 14p. 24443 L. Auslander/E. Feig/S. Winograd: The multiplicative complexity of the discrete Fourier transform. Adv. Appl. Math. 5 (1984), 31-55. 10063 L. Auslander/R. Tolimieri: Is computing with the finite Fourier transform pure or applied mathematics? Bull. AMS 1 (1979), 847-897. 24441 Ulrich Baum/Michael Clausen/Benno Tietz: Improved upper complexity bounds for the discrete Fourier transform. Internet 1990, 11p. 25344 A. Benz/.../D. Zardet: A broadband FFT spectrometer for radio and millimeter astronomy. Astronomy & Astrophysics 442 (2005), 767-773. 24433 Pascal Berger: Fast-Fourier-Transformation. Internet 2005, 14p. 24467 Glenn Bergland: A guided tour of the fast Fourier transform. IEEE Spectrum 6/7 (1969), 41-52. 24480 Daniel Bernstein: The tangent FFT. Springer LN CS 4851 (2007), 291-300. 24442 M. Bhattacharya/R. Creutzburg/J. Astola: Some historical notes on number theoretic transform. Internet, ca. 2005, 8p. R. Blahut: Fast algorithms for digital signal processing. Addison-Wesley 1985. 345 Ronald Bracewell: Die Fourier-Transformation. Spektrum 1989/8, 90-99. Ronald Bracewell: Schnelle Hartley-Transformation. Eine reellwertige Alternative zur FFT. Oldenbourg 1990, 260p. 3-486-21079-3. DM 68. 24464 William Briggs/Van Emden Henson: The DFT. SIAM 1995, 430p. Eur 40. " ... can be highly recommended ... " (H. Feichtinger) 16973 Elbert Brigham: The fast Fourier transform and its applications. Prentice-Hall 1988. 24424 C. Burrus (ed.): Fast Fourier transforms. Connexions, Rice Univ. 2012, 250p. 24176 R. Campello de Souza/H. de Oliveira/A. Kauffman: The Hartley transform in a finite field. Rev. Soc. Bras. Telecom. 14/1 (1999), 46-54. E. Chu/A. George: Inside the FFT black box. Springer 2000, 350p. DM 117. 8444 Barry Cipra: The FFT - making technology fly. SIAM News 26/3 (1993), ... M. Clausen/U. Baum: Fast Fourier transforms. Bibl. Inst. 1993, 190p. 3-411-16361-5. Ein Lehrbuch zum systematischen Entwurf schneller Fouriertransformationen ueber endlichen Gruppen. 24172 Michael Clausen/Ulrich Baum: Fast Fourier transform for symmetric groups - theory and implementation. Math. Comp. 61/204 (1993), 833-847. 24211 Michael Clausen/M. Müller: Generating fast Fourier transforms of solvable groups. J. Symb. Comp. 11 (2004), 1-18. 24455 Keith Conrad: Characters of finite abelian groups. Internet, 26p. A good mathematical exposition. 24493 James Cooley: The re-discovery of the fast Fourier transform. Mikrochimica Acta 3 (1987), 33-45. 24177 James Cooley/Peter Lewis/Peter Welch: The fast Fourier transform and its applications. IEEE Trans. Educ. 12/1 (1969), 27-34. 24492 James Cooley/Peter Lewis/Peter Welch: Historical notes on the fast Fourier transform. IEEE Trans. Audio Electroac. AU-15/2 (1967), 76-79. James Cooley/John Tukey: An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19 (1965), 297-301. 25341 Tomasz Czajkowski/Christopher Comis/Mohamed Kawokgy: Fast Fourier transform implementation for high speed astrophysics applications on FPGAs. Internet ca. 2001, 54p. 24243 Gilbert Demengel: Transformations de Fourier generalisees. Ellipses 1999, 290p. Eur 23. 24178 Pierre Duhamel/Martin Vetterli: Improved Fourier and Hartley transform algorithms - application to cyclic convolution of real data. IEEE Trans. Acoust. Speech Signal Proc. 35/6 (1987), 818-824. 8456 Douglas Elliott/K. Ramamohan Rao: Fast transforms. Academic Press 1982, 450p. $193. Contents: Introduction, Fourier series and Fourier transforms, Discrete Fourier transforms, Fast Fourier transform algorithms, FFT algorithms that reduce multiplications, DFT filter shapes and shaping, Spectral analysis using the FFT, Walsh-Hadamard transforms, The generalized transform, Discrete orthogonal transforms, Number theoretic transforms. P. Duhamel/M. Vetterli: Fast Fourier transforms - a tutorial review. Signal Processing 19 (1990), 259-299. 16015 Otto Forster: Algorithmische Zahlentheorie. Vieweg 1996, 280p. Eur 33. Contains a very clear exposition of FFT. 24473 Massimo Galuzzi: La trasformata rapida di Fourier e la divisione fra polinomi - l'algoritmo di C. M. Fiduccia. Internet 2009, 17p. Morven Gentleman/Gordon Sande: Fast Fourier transforms for fun and profit. ... (1966), ... I. Good: The interaction algorithm and practical Fourier series. J. Royal Stat. Soc. B 20 (1958), 361-372; 22 (1960), 372-375. I. Good: The relationship between two fast Fourier transforms. IEEE Trans. Comput. C-20 (1971), 310-317. 24444 Brian Gough: FFT algorithms. Internet 1997, 37p. 16984 S. Gudvangen: Practical applications of number theoretic transforms. Internet 1999, 6p. 25339 Rasmus Handberg: Numerical methods - FFT in astrophysics. Internet, 17p. 25343 Peter Hauschildt: Computational astrophysics - Fast Fourier Transform. Internet (Talk) 2013, 60p. 16971 Michael Heideman/Don Johnson/C. Burrus: Gauss and the history of the fast Fourier transform. Arch. Hist. Exact Sci. 34/3 (1985), 265-277. "... il lavoro di J.W. Cooley e J.W. Tukey risale all'aprile 1965. Tuttavia, ben presto ci si avvide che gia' nel 1942 era stato pubblicato un algoritmo simile da G.C. Danielson e C. Lanczos, i quali a loro volta facevano riferimento a due articoli di C. Runge del 1903 e del 1905. Ulteriori successive ricerche permisero alla fine di stabilire che procedure analoghe erano state usate gia' nel 1805 dal solito C.F. Gauss -- e' nota la battuta secondo cui quello della FFT sia stato il 1001-esimo algoritmo di Gauss!" (Paolo Marincola). 24429 Peter Henrici: Fast Fourier methods in computational complex analysis. SIAM Rev. 21 (1979), 481-527. 2251 Ellis Horowitz/Sartaj Sahni: Algorithmen. Springer 1981, 770p. Contains a good discussion of the FFT. Manfred Hüttenhofer/Matthias Lesch/Norbert Peyerimhoff: Mathematik in Anwendung mit C++. UTB 1994. In Buchhandlungen noch erhältlich. 9869 Bernd Jähne: Digitale Bildverarbeitung. Springer 1997, 590p. 3-540-61379-X. DM 68. 24478 David Kahaner: The fast Fourier transform by polynomial evaluation. J. Appl. Math. Phys. 29 (1978), 387-394. 25340 B. Klein/.../K. Menten: The APEX digital Fast Fourier Transform spectrometer. Astronomy & Astrophysics 454 (2006), L29-L32. 24196 Henning Kühl/Maurico Sacchi/Jürgen Fertig: The Hartley transform in seismic imaging. Geophysics 66/4 (2001), 1251-1257. 24447 K. Pavan Kumar/.../K. Ramamani: FFT algorithms - a survey. Int. J. Eng. Science 2/4 (2013), 22-26. 4391 John Lipson: Elements of algebra and algebraic computing. Benjamin/Cummings 1981. 24192 Mark Hyosun Mar: The fast Hartley transform. USALC Report 1990, 25p. 16964 David Maslen/Daniel Rockmore: Adapted diameters and the efficient computation of FFTs on groups. Internet 1995, 10p. 16961 David Maslen/Daniel Rockmore: Generalized FFTs - a survey of some recent results. Internet 1995, 55p. 16965 David Maslen/Daniel Rockmore: The Cooley-Tukey FFT and group theory. Notices AMS November 2001, 1151-1163. 24193 Todd Mateer: Fast Fourier transform algorithms with applications. PhD thesis Clemson Univ. 2008, 340p. 24453 R. Mutagi: Understanding the discrete Fourier transform. Internet 2004, 4p. 24439 Andre' Neubauer: DFT. Teubner 2012, 160p. Eur 27 (Ebook). 24514 Peter Nicholson: Algebraic theory of finite Fourier transforms. J. Computer Syst. Sci. 5 (1971), 524-547. 5031 W. Niethammer: Anwendungen der schnellen Fouriertransformation in der Numerik. 5028 Chatterji/, 63-80. 3356 Henri Nussbaumer: Fast Fourier transforms and convolution algorithms. Springer 1982. Ulrich Oberst: Explizite Rekursionsformeln zur schnellen Fouriertransformation. Actes Sem. Loth. Comb. 18 (1988), 119-126. Ulrich Oberst: The fast Fourier transform. Centro Matematico Vito Volterra, Univ. Roma II, Publ. 79 (1991), 1-42. Ulrich Oberst: Galois theory and the fast Gelfand transform. Centro Matematico Vito Volterra, Univ. Roma II, Publ. 99 (1992), 1-34. Ulrich Oberst: The optimal fast Gelfand, Fourier and Hartley transforms (FGT, FFT, FHT) and Galois theory. SLN Math., ca. 1996. 24438 Ulrich Oberst: The Fast Fourier transform. SIAM J. Control Opt. 46/2 (2007), 496-540. 24376 Massimo Picardello: Analisi armonica - aspetti classici e numerici. Internet 2013, 1360p. John Pollard: The fast Fourier transform in a finite field. Math. Comp. 25 (1971), 365-374. 6051 William Press/Saul Teukolsky/William Vetterling/Brian Flannery: Numerical recipes in C. Cambridge UP 1992. 20865 William Press/Saul Teukolsky/William Vetterling/Brian Flannery: Numerical recipes. Cambridge UP 2007, 1240p. Eur 43. 24195 Terry Ritter: Walsh-Hadamard transforms - a literature survey. Internet 1996, 9p. 16967 Daniel Rockmore/.../Peter Stadler: Fast Fourier transforms for fitness landscapes. Internet circa 2000, 18p. 16963 Daniel Rockmore: The FFT - an algorithm the whole family can use. Internet 2000, 5p. 16962 Daniel Rockmore: Recent progress and applications in group FFTs. Internet 2005, 27p. 24188 Hakob Sarukhanyan/Sos Agaian/Karen Egiazarian/Jaakko Astola: Reversible Hadamard transforms. Facta Univ. Nis El. En. 20/3 (2007), 309-330. 24415 Tomas Sauer: Einführung in die Signal- und Bildverarbeitung. Vorl. Univ. Passau 2012, 150p. 24430 H. Schwarz: Elementare Darstellung der schnellen Fouriertransformation. Computing 18 (1977), 107-116. 24445 Ivan Selesnick/C. Burrus: Automatic generation of prime length FFT programs. IEEE Trans. Signal Proc. 44/1 (1996), 14-24. 24440 Ivan Selesnick/Gerald Schuller: The discrete Fourier transform. Pages 37-78 in K. Rao/P. Yip (ed.): Transform and data compression handbook. CRC 2000, 400p. 24481 Colin Steel/Thomas Joy/Tom Clure: Teaching FFT principles in the physical chemistry laboratory. J. Chem. Education 67/10 (1990), 883-887. Gilbert Strang: Introduction to applied mathematics. Wellesley-Cambridge Press 1986. 16993 Volker Strehl: Diskrete und schnelle Fouriertransformation. Internet 1994, 35p. 24216 N. Sundararajan: Fourier and Hartley transforms - a mathematical twin. Indian J. Pure Appl. Math. 28/10 (1997), 1361-1365. 17027 Audrey Terras: Fourier analysis on finite groups and applications. Cambridge UP 2001, 440p. $23. 24218 Thomas Theußl/Robert Tobler/Eduard Gröller: The multi-dimensional Hartley transform as a basis for volume rendering. Internet ca. 1997, 8p. 24450 Richard Tolimieri: Multiplicative characters and the discrete Fourier transform. Adv. Appl. Math. 7 (1986), 344-380. 24448 Richard Tolimieri/Myoung An: Lesser known FFT algorithms. Pages 151-162 in J. Byrnes (ed): 20th Century Harmonic Analysis. Kluwer 2001. 17037 Richard Tolimieri/Myoung An/Chao Lu: Algorithms for discrete Fourier transforms and convolution. Springer 1997, 280p. 24462 Charles Van Loan: Computational frameworks for the fast Fourier transform. SIAM 1992, 270p. Eur 45. 24451 M. Vulis: Ring structures and the discrete Fourier transform. Adv. Appl. Math. 6 (1985), 350-372. James Walker: Fast Fourier transforms. CRC 1996, 450p. $80. 24240 Andrew Watson/Allen Poirson: Separable two-dimensional discrete Hartley transform. J. Opt. Soc. Am. A 3/12 (1986), 2001-2004. 24179 Wikipedia: Fast Walsh-Hadamard transform. Internet, 1p. 24187 Wikipedia: Hadamard transform. Internet 2013, 5p. 24454 M. Wong: Discrete Fourier analysis. Springer 2011, 180p. Eur 43 (Ebook). Frank Yates: The design and analysis of factorial experiments. Imp. Bur. Soil. Sci. Techn. Comm. 35 (1937), .... 24279 ZZ: Die Fouriertransformation. Internet, 15p. 24436 ZZ: Fast-Fourier-Transform (FFT). Internet, 24p. 24432 ZZ: Die diskrete Fouriertransformation (DFT). Internet, 38p. 24434 ZZ: DFT und FFT. Internet, 12p.