Discrete and continuous fourier transforms: Analysis, applications and fast algorithms

Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms

Volumn , Issue , 2008, Pages 1-399

  Chu, Eleanor ^a  

^a UNIVERSITY OF GUELPH   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

DIGITAL COMPUTERS; DIGITAL SIGNAL PROCESSING; FOURIER ANALYSIS;

APPLICATION AREA; DIGITAL FILTERING; DISCRETE CONVOLUTION; FAST ALGORITHMS; FAST FOURIER TRANSFORM ALGORITHM; GRAPHICAL ILLUSTRATIONS; PRIME FACTORS; PRIOR KNOWLEDGE;

DISCRETE FOURIER TRANSFORMS;

EID: 85057704624     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (56)

1. A. Ambardar. Analog and Digital Signal Processing. Brooks/Cole Publishing Company, Paci c Grove, CA, second edition, 1999.
2. C. Anderson and M. D. Dahleh. Rapid computation of the discrete Fourier transform. SIAM J. Sci. Comput., 17(4):913 919, 1996.
3. J. Arsac. Fourier Transforms and the Theory of Distributions. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1966.
4. G. D. Bergland. The fast Fourier transform recursive equations for arbitrary length records. Math. Comp., 21(98):236 238, 1967.
5. L. L. Bluestein. A linear ltering approach to the computation of discrete Fourier transform. IEEE Transactions on Audio and Electroacoustics, AU-18:451 455, 1970. Reprinted in Digital Signal Processing, Eds. L. R. Rabimer and C. M. Rader, pp. 317 321, IEEE Press, New York, 1972.
6. R. N. Bracewell. The Fourier Transform and Its Applications. McGraw-Hill Inc., San Francisco, CA, third edition, 2000.
7. W. L. Briggs and V. E. Hensen. The DFT: An Owner’s Manual for the Discrete Fourier Transform. The Society for Industrial and Applied Mathematics, Philadelphia, PA, 1995.
8. E. O. Brigham. The Fast Fourier Transform and Its Applications. Prentice-Hall, Inc., Upper Saddle River, NJ, 1988.
9. C. S. Burrus and P. W. Eschenbacher. An in-place, in-order prime factor FFT algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-29:806 817, 1981.
10. T. Butz. Fourier Transformation for Pedestrians. Springer-Verlag, Berlin, 2006.
11. D. C. Champeney. Fourier Transforms and Their Physical Applications. AcademicPress Inc., London, UK, 1973.
12. D. C. Champeney. AHandbook of Fourier Theorems. Cambridge University Press, Cambridge, UK, 1987.
13. E. Chu and A. George. Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms. CRC Press, Boca Raton, FL, 2000.
14. R. V. Churchill. Fourier Series and Boundary Value Problems. McGraw-Hill Book Company, Inc., New York, second edition, 1963.
15. J. W. Cooley, P. A. W. Lewis, and P. D. Welch. Historical notes on the fast Fourier transform. IEEE Trans. Audio and Electroacoustics, 15:76 79, 1967.
16. J. W. Cooley and J. W. Tukey. An algorithm for the machine calculation of complex Fourier series. Math. Comp., 19:297 301, 1965.
17. H. F. Davis. Fourier Series and Orthogonal Functions. Allyn and Bacon, Inc., Boston, MA, 1963.
18. C. de Boor. FFT as nested multiplications, with a twist. SIAM J. Sci. Stat. Comput., 1:173 178, 1980.
19. A. Deitmar. AFirstCourse in Harmonic Analysis. Springer-Verlag, New York, second edition, 2005.
20. M. Frigo and S. G. Johnson. FFTW: An adaptive software architecture for the FFT. In Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, volume 3, pp. 1381 1384, 1998.
21. D. Gabor. Theory of communication. J.I.E.E., 93(Part III):492 444, 1946.
22. R. R. Goldberg. Fourier Transforms. Cambridge University Press, Cambridge, UK, 1965.
23. R. C. Gonzales and R. E. Woods. Digital Image Processing. Addison-Wesley Publishing Company, Reading, MA, 1992.
24. I. J. Good. The interaction algorithm and practical Fourier analysis. J. Roy. Statist. Soc., Ser. B, 20:361 372, 1958. Addendum, 22:372 375, 1960.
25. J. C. Goswami and A. K. Chan. Fundamentals of Wavelets. John Wiley & Sons, Inc., NewYork, 1999.
26. A. Graham. Kronecker Products and Matrix Calculus with Applications. Ellis Horwood Limited, West Sussex, UK, 1981.
27. R. W. Hamming. Digital Filters. Prentice-Hall, Inc., Englewood Cliffs, NJ, third edition, 1989.
28. D. J. Higham and N. J. Higham. The MATLAB Guide. The Society for Industrial and Applied Mathematics, Philadelphia, PA, 2000.
29. D. J. Higham and N. J. Higham. The MATLAB Guide. 2nd ed., The Society for Industrial and Applied Mathematics, Philadelphia, PA, 2005.
30. FFTW: The Fastest Fourier Transform in the West. http://www.fftw.org/.
31. D. P. Kolba and T. W. Parks. A prime factor algorithm using high-speed convolution. IEEE Trans. Acoust. Speech Signal Process, ASSP-25:281 294, 1977.
32. C. F. Van Loan. Computational Frameworks for the Fast Fourier Transform. TheSociety for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
33. J. H. McClellan and C. M. Rader. Number Theory in Digital Signal Processing. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1979.
34. Y. Nievergelt. Wavelets Made Easy. Birkh¤auser Boston, Cambridge, MA, 1999.
35. H. J. Nussbaumer. Fast Fourier Transform and Convolution Algorithms. Springer Series in Information Sciences. Springer-Verlag, Berlin, 1981.
36. J. S. Otto. Symmetric prime factor fast Fourier transform algorithms. SIAM J. Sci. Stat. Comput., 19:419 431, 1989.
37. A. Papoulis. The Fourier Integral and Its Applications. McGraw-Hill Book Company, Inc., New York, 1962.
38. B. Porat. ACourse in Digital Signal Processing. John Wiley & Sons, Inc., New York, 1997.
39. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C++: The Art of Scientific Computing. Cambridge University Press, Cambridge, UK, second edition, 2001.
40. J. N. Rayner. An Introduction to Spectral Analysis. PionLimited, London, UK, 1971.
41. J. H. Rothweiler. Implementation of the in-order prime factor transform for variable sizes. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-30:105 107, 1982.
42. E. M. Stein and G. Weiss. Introduction to Fourier Analysis on Euclidean Spaces. Prince-tonUniversity Press, Princeton, NJ, 1971.
43. P. N. Swarztrauber, R. A. Sweet, W. L. Briggs, V. E. Henson, and J. Otto. Bluestein s FFT for arbirary N on the hypercube. Parallel Computing, 17:607 617, 1991.
44. C. Temperton. Self-sorting mixed-radix fast Fourier transforms. J. of Computational Physics, 52:1 23, 1983.
45. C. Temperton. Implementation of a self-sorting in-place prime factor FFT algorithm. J. of Computational Physics, 58:283 299, 1985.
46. C. Temperton. Implementation of a prime factor FFT algorithm on Cray-1. Parallel Computing, 6:99 108, 1988.
47. C. Temperton. A new set of minimum-add small-n rotated DFT modules. J. of Computational Physics, 75:190 198, 1988.
48. C. Temperton. A self-sorting in-place prime factor real/half-complex FFT algorithm. J. of Computational Physics, 75:199 216, 1988.
49. C. Temperton. Self-sorting in-place fast Fourier transforms. SIAM J. Sci. Comput., 12:808 823, 1991.
50. r. SIAM J. Sci. Comput., 13:676 686, 1992.
51. E. C. Titchmarsh. Introduction to the Theory of Fourier Integrals. Clarendon Press, Oxford, UK, 1962.
52. J. S. Walker. Fourier Analysis. Oxford University Press, New York, 1988.
53. H. J. Weaver. Applications of Discrete and Continuous Fourier Analysis. John Wiley & Sons, Inc., New York, 1983.
54. H. J. Weaver. Theory of Discrete and Continuous Fourier Analysis. John Wiley & Sons, Inc., New York, 1989.
55. S. Winograd. On computing the DFT. Math. Comp., 32:175 199, 1978.
56. C. R. Wylie. Advanced Engineering Mathematics. McGraw-Hall Book Company, New York, fourth edition, 1975.