Index
DFT Matrix in Matlab
Mathematics of the Discrete Fourier Transform (DFT)
Contents
Global
Contents
Global
Index Index Search
-
- 1
- J. O. Smith III,
Introduction to Digital Filters,
http://www-ccrma.stanford.edu/~jos/filters/,
2003.
- 2
- R. V. Churchill,
Complex
Variables and Applications,
McGraw-Hill, New York, 1960.
- 3
- W. R. LePage,
Complex
Variables and the Laplace
Transform for Engineers,
Dover, New York, 1961.
- 4
- K. Steiglitz,
A Digital Signal Processing Primer
with Applications to Audio and Computer Music,
Addison-Wesley,
Reading MA, 1996.
- 5
- J. R. Pierce,
``private communication'', 1991.
- 6
- J. O. Smith III,
Digital
Waveguide Modeling of Musical Instruments,
http://www-ccrma.stanford.edu/~jos/waveguide/,
2003.
- 7
- S. M. Kay,
Fundamentals of Statistical
Signal Processing, Volume I: Estimation Theory,
Prentice-Hall,
Inc., Englewood Cliffs, NJ, 1993.
- 8
- L. L. Sharf,
Statistical
Signal Processing, Detection, Estimation, and Time Series Analysis,
Addison-Wesley, Reading MA, 1991.
- 9
- B. Noble,
Applied Linear
Algebra,
Prentice-Hall, Inc., Englewood Cliffs, NJ, 1969.
- 10
- M. Abramowitz and I. A. Stegun, Eds.,
Handbook of
Mathematical Functions,
Dover, New York, 1965.
- 11
- J. O. Smith and P. Gossett,
``A flexible sampling-rate
conversion method'',
in Proceedings of the International
Conference on Acoustics, Speech, and Signal Processing, San Diego, New
York, March 1984, vol. 2, pp. 19.4.1-19.4.2, IEEE Press,
expanded
tutorial and associated free software available at the Digital Audio Resampling
Home Page: http://www-ccrma.stanford.edu/~jos/resample/.
- 12
- A. Papoulis,
Signal Analysis,
McGraw-Hill, New York,
1977.
- 13
- F. J. Harris,
``On the use of windows for harmonic
analysis with the discrete
Fourier transform'',
Proceedings of the IEEE, vol. 66, no. 1,
pp. 51-83, Jan 1978.
- 14
- R. Bracewell,
The Fourier
Transform and its Applications,
McGraw-Hill, New York, 1965.
- 15
- E. O. Brigham,
The Fast
Fourier Transform,
Prentice-Hall, Inc., Englewood Cliffs, NJ,
1974.
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- D. C. Champeney,
A Handbook of Fourier
Theorems,
Cambridge University Press, 1987.
- 17
- W. Rudin,
Principles of Mathematical Analysis,
McGraw-Hill, New York, 1964.
- 18
- M. H. Protter and J. Charles B. Morrey,
Modern
Mathematical Analysis,
Addison-Wesley, Reading MA, 1964.
- 19
- M. Unser,
``Splines: A perfect fit for signal and image
processing'',
assp_magazine, vol. 16, no. 6, pp. 22-38, November
1999.
- 20
- J. Gullberg,
Mathematics From the Birth of Numbers,
Norton and Co., New York, 1997,
[Qa21.G78 1996] ISBN 0-393-04002-X.
- 21
- A. D. Pierce,
Acoustics,
American Institute of Physics, for the Acoustical
Society of America, http://asa.aip.org/publications.html, 1989.
- 22
- S. S. Stevens and H. Davis,
Hearing:
It's Psychology and Physiology,
American Institute of Physics, for the Acoustical
Society of America, http://asa.aip.org/publications.html, 1983,
Copy of original 1938 edition.
- 23
- K. Brandenburg and M. Bosi,
``Overview of MPEG audio: Current and future standards for
low-bit-rate audio coding'',
Journal of the Audio Engineering
Society, vol. 45, no. 1/2, pp. 4-21, Jan./Feb. 1997.
- 24
- T. Painter and A. Spanias,
``Perceptual coding of digital
audio'',
Proceedings of the IEEE, vol. 88, no. 4, pp. 451-513,
April 2000.
- 25
- L. Bosse,
``An experimental high fidelity perceptual audio
coder'',
Tech. Rep., Elec. Engineering Dept., Stanford University (CCRMA), March 1998,
Music 420
Project Report, available online at http://www-ccrma.stanford.edu/~jos/bosse/.
- 26
- J. P. Campbell Jr., T. E. Tremain, and V. C. Welch,
``The proposed federal standard 1016 4800 bps voice coder: Celp'',
Speech Technology Magazine, pp. 58-64, April-May 1990.
- 27
- J. Makhoul,
``Linear
prediction: A tutorial review'',
Proceedings of the IEEE,
vol. 63, pp. 561-580, April 1975.
- 28
- J. D. Markel and A. H. Gray,
Linear
Prediction of Speech,
Springer Verlag, New York, 1976.
- 29
- H. W. Strube,
``Linear
prediction on a warped frequency scale'',
Journal of the
Acoustical Society of America, vol. 68, no. 4, pp. 1071-1076, 1980.
- 30
- J. Dattorro,
``The implementation of recursive digital filters for
high-fidelity audio'',
Journal of the Audio Engineering Society,
vol. 36, pp. 851-878, Nov. 1988,
Comments, ibid. (Letters to the Editor),
vol. 37, p. 486 (1989 June); Comments, ibid. (Letters to the Editor), vol. 38,
pp. 149-151 (1990 Mar.).
- 31
- L. R. Rabiner and R. W. Schafer,
Digital Processing of
Speech Signals,
Prentice-Hall, Englewood Cliffs, NJ, 1978.
- 32
- A. Papoulis,
Probability, Random Variables, and Stochastic
Processes,
McGraw-Hill, New York, 1965.
- 33
- T. Kailath, A. H. Sayed, and B. Hassibi,
Linear
Estimation,
Prentice-Hall, Inc., Englewood Cliffs, NJ, April 2000.
- 34
- G. H. Golub and C. F. Van Loan,
Matrix
Computations, 2nd Edition,
The Johns Hopkins University Press,
Baltimore, 1989.
- 35
- S. M. Kay,
Modern Spectral Estimation,
Prentice-Hall, Inc., Englewood Cliffs, NJ, 1988.
- 36
- P. D. Welch,
``The use of fast
Fourier transforms for the estimation of power spectra:
A method based on time averaging over short modified periodograms'',
IEEE Transactions on Audio and Electroacoustics, vol. 15, pp.
70-73, 1967,
reprinted in [59]
and [60].
- 37
- L. Ljung and T. L. Soderstrom,
Theory and Practice of
Recursive Identification,
MIT Press, Cambridge, MA, 1983.
- 38
- J. O. Smith III,
Mathematics of the Discrete Fourier Transform
(DFT),
http://www-ccrma.stanford.edu/~jos/mdft/, 2003.
- 39
- M. J. Lighthill,
Introduction to Fourier
Analysis,
Cambridge University Press, January 1958.
- 40
- M. Heideman, D. Johnson, and C. S. Burrus,
``Gauss and
the history of the FFT'',
IEEE Signal Processing Magazine, vol. 1, no. 3, pp. 14-21,
October 1984,
also in the Archive for History of Exact Sciences,
vol. 34, no. 3, pp. 265-277, 1985.
- 41
- J. Cooley and J. Tukey,
``An algorithm for the machine
computation of the complex Fourier
series'',
Mathematics of Computation, vol. 19, pp. 297-301,
April 1965.
- 42
- H. V. Sorenson, M. T. Heideman, and C. S. Burrus,
``On
calculating the split-radix
fft'',
IEEE Transactions on Acoustics, Speech, Signal Processing, vol.
ASSP-34, pp. 152-156, Feb. 1986.
- 43
- J. H. McClellan and C. M. Rader,
Number Theory in Digital Signal Processing,
Prentice-Hall, Inc., Englewood Cliffs, NJ, 1979.
- 44
- C. S. Burrus and T. W. Parks,
DFT/FFT
and Convolution
Algorithms,
John Wiley and Sons, Inc., New York, 1985.
- 45
- M. Bosi and R. E. Goldberg,
Introduction to Digial Audio
Coding and Standards,
Kluwer Academic Publishers, Boston, 2003.
- 46
- P. Duhamel and M. Vetterli,
``Improved Fourier and Hartley
algorithms with application to cyclic convolution
of real data'',
IEEE Transactions on Acoustics, Speech, Signal
Processing, vol. 35, pp. 818-824, June 1987.
- 47
- R. Agarwal and C. S. Burrus,
``Number theoretic transforms to
implement fast digital convolution'',
Proceedings of the IEEE, vol. 63, pp. 550-560, April 1975,
also in [43].
- 48
- D. Kolba and T. Parks,
``A prime factor FFT
algorithm using high-speed convolution'',
IEEE Transactions on Acoustics, Speech, Signal Processing, vol.
29, pp. 281-294, August 1977,
also in [43].
- 49
- P. Duhamel and M. Vetterli,
``Fast
Fourier transforms: A tutorial review and state of the art'',
Signal Processing, vol. 19, pp. 259-299, April 1990.
- 50
- H. V. Sorenson, D. L. Jones, M. T. Heideman, and C. S.
Burrus,
``Real-valued fast
fourier transform algorithms'',
IEEE Transactions on Acoustics,
Speech, Signal Processing, vol. ASSP-35, no. 6, pp. 849-863, June 1987.
- 51
- C. S. Burrus,
``Notes on the fft'',
March 1990.
- 52
- S. Johnson,
Prime-Factor FFT
Algorithm,
http://www.wikipedia.org/wiki/Prime-factor_FFT_
algorithm, 2003.
- 53
- 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, Seattle, New York, 1998, vol. 3, pp.
1381-1384, IEEE Press,
available online at http://www.fftw.org/.
- 54
- J. H. McClellan, R. W. Schafer, and M. A. Yoder,
DSP First: A Multimedia
Approach,
Prentice-Hall, Englewood Cliffs, NJ, 1998,
Tk5102.M388.
- 55
- C. Roads, Ed.,
The Music Machine,
MIT Press,
Cambridge, MA, 1989.
- 56
- H. L. F. von Helmholtz,
Die Lehre von den
Tonempfindungen als Physiologische Grundlage für die Theorie der Musik,
F. Vieweg und Sohn, Braunschweig, 1863.
- 57
- C. Roads,
The Computer Music Tutorial,
MIT Press,
Cambridge, MA, 1996.
- 58
- N. H. Fletcher and T. D. Rossing,
The Physics of Musical
Instruments, Second Edition,
Springer Verlag, New York, 1998,
485
illustrations, hardcover, 69.95 USD direct from Springer.
- 59
- D. G. Childers, Ed.,
Modern Spectrum
Analysis,
IEEE Press, New York, 1978.
- 60
- L. R. Rabiner and C. M. Rader, Eds.,
Digital Signal Processing,
IEEE Press, New York, 1972.
Index
DFT Matrix in Matlab
Mathematics of the Discrete Fourier Transform (DFT)
Contents
Global
Contents
Global
Index Index Search
``Mathematics of the Discrete
Fourier Transform (DFT)'', by Julius O. Smith III, (online
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