Bibliography for the Fast Fourier Transform

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  1. Description of dental arch form using the Fourier series
    Valenzuela A, P.; Pardo, M. A.; Yezioro, S.
    International Journal of Adult Orthodontics and Orthognathic Surgery, 2002, vol. 17, no. 1, pp. 59-65 , Ingenta.  
  2. The Cooley-Tukey FFT and group theory.  
    Maslen, David K.; Rockmore, Daniel N.
    Notices Amer. Math. Soc. 48 (2001), no. 10, 1151--1160, Math. Sci. Net.  
  3. Teaching time-series analysis. I. Finite Fourier analysis of ocean waves
    Whitford, D. J.; Vieira, M. E. C.; Waters, J. K.
    American Journal of Physics, 2001, vol. 69, no. 4, pp. 490-496 , Ingenta.  
  4. Applications of Fourier Series in Classical Guitar Technique  
    James Hughes  
    College Math Journal: 2000, Volume 31, Number 4, Pages: 300-303.  
  5. Lesser known FFT algorithms.
    Tolimieri, R.; An, M.
    Twentieth century harmonic analysis---a celebration (Il Ciocco, 2000), 151--162, NATO Sci. Ser. II Math. Phys. Chem., 33, Kluwer Acad. Publ., Dordrecht, 2001, Math. Sci. Net.  
  6. The future fast Fourier transform ?
    Edelman, Alan; McCorquodale, Peter; Toledo, Sivan
    SIAM J. Sci. Comput. 20 (1999), no. 3, 1094--1114 (electronic).
  7. Two- and three-dimensional image rotation using the FFT.
    Cox, Robert W.; Tong, Raoqiong
    IEEE Trans. Image Process. 8 (1999), no. 9, 1297--1299, Math. Sci. Net.  
  8. Pepinsky's Machine: an interactive graphics-based Fourier synthesis program with applications in teaching and research.
    Glykos, N. M.
    Journal of applied crystallography, 1999, vol. 32p4, pp. 821 , Ingenta.  
  9. On numerical methods for discrete least-squares approximation by trigonometric polynomials.    
    Fassbender, Heike    
    Math. Comp. 66 (1997), no. 218, 719--741, Math. Sci. Net.  
  10. Configurational transitions in Fourier series-represented DNA supercoils.
    Liu, Guohua; Schlick, Tamar; Olson, Wilma K.
    Biophysical journal, 1997, vol. 73, no. 4, pp. 1742 , Ingenta.  
  11. A note on Newbery's algorithm for discrete least-squares approximation by trigonometric polynomials.    
    Faßbender, Heike    
    Electron. Trans. Numer. Anal. 4 (1996), June, 64--74 (electronic), Math. Sci. Net.  
  12. On the L^2 Inequalities Involving Trigonometric Polynomials and Their Derivatives  
    Weiyu Chen  
    Transactions of the American Mathematical Society, Vol. 347, No. 5. (May, 1995), pp. 1753-1761, Jstor.  
  13. Determining the number of terms in a trigonometric regression.    
    Kavalieris, L.; Hannan, E. J.    
    J. Time Ser. Anal. 15 (1994), no. 6, 613--625, Math. Sci. Net.  
  14. Fast Fourier Transforms for Symmetric Groups: Theory and Implementation  
    Michael Clausen, Ulrich Baum  
    Mathematics of Computation, Vol. 61, No. 204. (Oct., 1993), pp. 833-847, Jstor.  
  15. FFT-Based Preconditioners for Toeplitz-Block Least Squares Problems  
    Raymond H. Chan, James G. Nagy, Robert J. Plemmons  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 6. (Dec., 1993), pp. 1740-1768, Jstor.  
  16. FFT in calculating nonparametric regression estimate based on trigonometric series.
    Rafajowicz, Ewaryst; Skubalska-Rafajowicz, Ewa
    Appl. Math. Comput. Sci. 3 (1993), no. 4, 713--720, Math. Sci. Net.  
  17. On approximation by trigonometric Lagrange interpolating polynomials. II.    
    Borwein, P. B.; Xie, T. F.; Zhou, S. P.    
    Bull. Austral. Math. Soc. 45 (1992), no. 2, 215--221, Math. Sci. Net.  
  18. Discrete Least Squares Approximation by Trigonometric Polynomials  
    L. Reichel, G. S. Ammar, W. B. Gragg  
    Mathematics of Computation, Vol. 57, No. 195. (Jul., 1991), pp. 273-289, Jstor.  
  19. The Fractional Fourier Transform and Applications  
    David H. Bailey, Paul N. Swarztrauber  
    SIAM Review, Vol. 33, No. 3. (Sep., 1991), pp. 389-404, Jstor.  
  20. A Stochastic Roundoff Error Analysis for the Fast Fourier Transform  
    Daniela Calvetti  
    Mathematics of Computation, Vol. 56, No. 194. (Apr., 1991), pp. 755-774, Jstor.  
  21. Algorithm AS 265:  G/G/1 Via Fast Fourier Transform (in Statistical Algorithms)  
    R. Grubel  
    Applied Statistics, Vol. 40, No. 2. (1991), pp. 355-365, Jstor.  
  22. Tests of Distributional Hypotheses with Nuisance Parameters Using Fourier Series Methods (in Theory and Methods)  
    Bryan Langholz, Richard A. Kronmal  
    Journal of the American Statistical Association, Vol. 86, No. 416. (Dec., 1991), pp. 1077-1084, Jstor.  
  23. Transforms, Finite Fields, and Fast Multiplication  
    Patrick Chu  
    Mathematics Magazine: 1990, Volume 63, Number 5, Pages: 330-336.  
  24. Curve Fitting by Polynomial-Trigonometric Regression  
    R. L. Eubank, Paul Speckman  
    Biometrika, Vol. 77, No. 1. (Mar., 1990), pp. 1-9, Jstor.  
  25. The FFT as a Multigrid Algorithm  
    William L. Briggs, Van Emden Henson  
    SIAM Review, Vol. 32, No. 2. (Jun., 1990), pp. 252-261, Jstor.  
  26. An Algorithm Based on the FFT for a Generalized Chebyshev Interpolation  
    Takemitsu Hasegawa, Tatsuo Torii, Hiroshi Sugiura  
    Mathematics of Computation, Vol. 54, No. 189. (Jan., 1990), pp. 195-210, Jstor.  
  27. An FFT Extension to the P-1 Factoring Algorithm  
    Peter L. Montgomery, Robert D. Silverman  
    Mathematics of Computation, Vol. 54, No. 190. (Apr., 1990), pp. 839-854, Jstor.  
  28. Curve fitting by polynomial-trigonometric regression.    
    Eubank, R. L.; Speckman, Paul    
    Biometrika 77 (1990), no. 1, 1--9, Math. Sci. Net.  
  29. Fast Fourier transforms: a tutorial review and a state of the art.
    Duhamel, P.; Vetterli, M.
    Signal Process. 19 (1990), no. 4, 259--299.
  30. On approximation by trigonometric Lagrange interpolating polynomials.    
    Xie, T. F.; Zhou, S. P.    
    Bull. Austral. Math. Soc. 40 (1989), no. 3, 425--428, Math. Sci. Net.  
  31. Remark AS R73: A Remark on Algorithm AS 222: Resistant Smoothing Using the Fast Fourier Transform (in Statistical Algorithms)  
    Tony Dusoir  
    Applied Statistics, Vol. 37, No. 2. (1988), pp. 316-317, Jstor.  
  32. Algorithm AS 222: Resistant Smoothing Using the Fast Fourier Transform (in Statistical Algorithms)  
    W. Hardle  
    Applied Statistics, Vol. 36, No. 1. (1987), pp. 104-111, Jstor.  
  33. Approximation properties of some trigonometric polynomials.   
    Taberski, Roman    
    Funct. Approx. Comment. Math. 17 (1987), 83--95, Math. Sci. Net.  
  34. Computer Graphics for the Vibrating String  
    Howard Lewis Penn  
    College Math Journal: 1986, Volume 17, Number 1, Pages: 79-89.  
  35. Remark ASR 64: A Remark on Algorithm AS 176: Kernel Density Estimation Using The Fast Fourier Transform (in Statistical Algorithms)  
    Paul Schiffelbein  
    Applied Statistics, Vol. 35, No. 2. (1986), pp. 235-236, Jstor.  
  36. Application of Fourier series to curve fitting. (Spanish)  
    Soto Villaverde, Andrés; Cuesta Saínz de la Torre, Lylia E.
    Investigación Oper. 7 (1986), no. 3, 17--28, MathSciNet.  
  37. The discrete Fourier transform, the FFT and the solution of differential equations. (Spanish)
    Mora E., Héctor M.
    Bol. Mat. 20 (1986), no. 2, 107--123, MathSciNet.  
  38. Optimal Designs for Trigonometric and Polynomial Regression Using Canonical Moments  
    Tai-Shing Lau, W. J. Studden  
    Annals of Statistics, Vol. 13, No. 1. (Mar., 1985), pp. 383-394, Jstor.  
  39. Mathematical Considerations for the Problem of Fourier Transform Phase Retrieval from Magnitude  
    Jorge L. C. Sanz  
    SIAM Journal on Applied Mathematics, Vol. 45, No. 4. (Aug., 1985), pp. 651-664, Jstor.  
  40. Remark AS R50: A Remark on Algorithm AS 176. Kernal Density Estimation Using the Fast Fourier Transform (in Statistical Algorithms)  
    M. C. Jones, H. W. Lotwick  
    Applied Statistics, Vol. 33, No. 1. (1984), pp. 120-122, Jstor.  
  41. On the Degree of Approximation of a Class of Functions by Means of Fourier Series  
    S. M. Mazhar  
    Proceedings of the American Mathematical Society, Vol. 88, No. 2. (Jun., 1983), pp. 317-320, Jstor.  
  42. Algorithm AS 176: Kernel Density Estimation Using the Fast Fourier Transform (in Statistical Algorithms)  
    B. W. Silverman  
    Applied Statistics, Vol. 31, No. 1. (1982), pp. 93-99, Jstor.  
  43. Fast Algorithm of Data Permutation in Discrete Fast Fourier Transform (in Statistical Algorithms)  
    Andrzej Francik, Janusz Koscielniak  
    Applied Statistics, Vol. 31, No. 3. (1982), pp. 327-330, Jstor.  
  44. A Vector Implementation of the Fast Fourier Transform Algorithm  
    Bengt Fornberg  
    Mathematics of Computation, Vol. 36, No. 153. (Jan., 1981), pp. 189-191, Jstor.  
  45. Computing the Fast Fourier Transform on a Vector Computer  
    David G. Korn, Jules J. Lambiotte, Jr.  
    Mathematics of Computation, Vol. 33, No. 147. (Jul., 1979), pp. 977-992, Jstor.  
  46. Least Squares Fourier Series Solutions to Boundary Value Problems  
    Robert B. Kelman  
    SIAM Review, Vol. 21, No. 3. (Jul., 1979), pp. 329-338, Jstor.  
  47. Basic Fourier Series  
    H. Exton  
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 369, No. 1736. (Dec. 13, 1979), pp. 115-136, Jstor.  
  48. Fast Fourier Methods in Computational Complex Analysis  
    Peter Henrici  
    SIAM Review, Vol. 21, No. 4. (Oct., 1979), pp. 481-527, Jstor.  
  49. On the Degree of Approximation of a Function by the Partial Sums of its Fourier Series  
    Elaine Cohen  
    Transactions of the American Mathematical Society, Vol. 235. (Jan., 1978), pp. 35-74, Jstor.  
  50. On Computing the Discrete Fourier Transform  
    S. Winograd  
    Mathematics of Computation, Vol. 32, No. 141. (Jan., 1978), pp. 175-199, Jstor.
  51. The Fast Fourier Transform Spectral Estimator (in Notes, Comments and Queries)  
    Piet De Jong  
    Journal of the Royal Statistical Society. Series B (Methodological), Vol. 39, No. 3. (1977), pp. 327-330, Jstor.
  52. A Table of Discrete Fourier Transform Pairs  
    Brian Conolly, I. J. Good  
    SIAM Journal on Applied Mathematics, Vol. 32, No. 4. (Jun., 1977), pp. 810-822, Jstor.
  53. On Computing the Discrete Fourier Transform  
    Shmuel Winograd  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 73, No. 4. (Apr., 1976), pp. 1005-1006, Jstor.
  54. Algorithm AS 97: Real Discrete Fast Fourier Transform (in Statistical Algorithms)  
    Donald M. Monro  
    Applied Statistics, Vol. 25, No. 2. (1976), pp. 166-172, Jstor.
  55. Algorithm AS 83: Complex Discrete Fast Fourier Transform (in Statistical Algorithms)  
    Donald M. Monro  
    Applied Statistics, Vol. 24, No. 1. (1975), pp. 153-160, Jstor.
  56. Roundoff Error Analysis of the Fast Fourier Transform  
    George U. Ramos  
    Mathematics of Computation, Vol. 25, No. 116. (Oct., 1971), pp. 757-768, Jstor.  
  57. The Fast Fourier Transform in a Finite Field  
    J. M. Pollard  
    Mathematics of Computation, Vol. 25, No. 114. (Apr., 1971), pp. 365-374, Jstor.  
  58. Trigonometric Interpolation and Curve-Fitting  
    A. C. R. Newbery  
    Mathematics of Computation, Vol. 24, No. 112. (Oct., 1970), pp. 869-876, Jstor.  
  59. Trigonometric interpolation and curve-fitting.    
    Newbery, A. C. R.    
    Math. Comp. 24 1970 869--876, Math. Sci. Net.  
  60. A Fast Fourier Transform Algorithm Using Base 8 Iterations  
    G. D. Bergland  
    Mathematics of Computation, Vol. 22, No. 102. (Apr., 1968), pp. 275-279, Jstor.  
  61. Application of Fourier Series to Summation of Series.  
    Edstrom,Clarence R.  
    Mathematics Magazine 40 (1967) 214-216.
  62. The Fast Fourier Transform Recursive Equations for Arbitrary Length Records (in Technical Notes and Short Papers)  
    G. D. Bergland  
    Mathematics of Computation, Vol. 21, No. 98. (Apr., 1967), pp. 236-238, Jstor.  
  63. Curve fitting to unequally-spaced data: Polynomial and trigonometric approximation.    
    Oliveira-Pinto, F.    
    Inst. Gulbenkian Ci. Centro Cálc. Ci. Estud. Program. Anál. Numér. No. 2 1967 47--59, Math. Sci. Net.  
  64. Interpolation by Algebraic and Trigonometric Polynomials (in Technical Notes and Short Papers)  
    A. C. R. Newbery  
    Mathematics of Computation, Vol. 20, No. 96. (Oct., 1966), pp. 597-599, Jstor.  
  65. Analogue Calculation of Polynomial and Trigonometric Expansions (in Other Aids to Computation)  
    Max G. Scherberg, John F. Riordan  
    Mathematical Tables and Other Aids to Computation, Vol. 7, No. 41. (Jan., 1953), pp. 61-65, Jstor.  
  66. Note on Invariance of Degree of Polynomial and Trigonometric Approximation under Change of Independent Variable  
    J. L. Walsh  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 45, No. 10. (Oct. 15, 1959), pp. 1528-1533, Jstor.  
  67. Analogue Calculation of Polynomial and Trigonometric Expansions (in Other Aids to Computation)  
    Max G. Scherberg, John F. Riordan  
    Mathematical Tables and Other Aids to Computation, Vol. 7, No. 41. (Jan., 1953), pp. 61-65, Jstor.  
  68. Infinite Series and Taylor and Fourier Expansions.  
    James, Robert C.
    Mathematics Magazine 25 (1952) 269-272;26 (1952) 21-31.  
  69. Certain Expressions Related to Fourier Series.  
    Dobbie, J. M.  
    Mathematics Magazine 17 (1943) 285-291.  
  70. Some Introductory Exercises in the Manipulation of Fourier Transforms.  
    Cameron, Robert H.  
    Mathematics Magazine 15 (1941) 331-356.  
  71. On the Convergence of Certain Trigonometric and Polynomial Approximations  
    Dunham Jackson  
    Transactions of the American Mathematical Society, Vol. 22, No. 2. (Apr., 1921), pp. 158-166, Jstor.  
  72. On Approximation by Trigonometric Sums and Polynomials  
    Dunham Jackson  
    Transactions of the American Mathematical Society, Vol. 13, No. 4. (Oct., 1912), pp. 491-515, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003