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comp.compression Frequently Asked Questions (part 1/3)
Section - [25] Fast DCT (Discrete Cosine Transform) algorithms

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Many image compression methods, including the JPEG, MPEG, and H.261 standards,
are based on the discrete cosine transform.  A good overall introduction to
DCT is the book "Discrete Cosine Transform---Algorithms, Advantages,
Applications" by K.R. Rao and P. Yip (Academic Press, London, 1990),
ISBN 0-12-580203-X. This has an extensive, though already dated, bibliography.

Here are some references mostly provided by Tom Lane <tgl@sss.pgh.pa.us>.
(This list is now rather dated.)
Most of these are in IEEE journals or conference proceedings, notably
ICASSP = IEEE Intl. Conf. on Acoustics, Speech, and Signal Processing.
ICCAS = IEEE Intl. Conf. on Circuits and Systems.
DCC = Data Compression Conference.

Polynomial Transform Computation of the 2-D DCT, Duhamel & Guillemot,
  ICASSP '90 p. 1515.
A Forward-Mapping Realization of the Inverse DCT, McMillan & Westover,
  DCC '92 p. 219.
A Fast Algorithm for 2-D DCT, Cho, Yun & Lee, ICASSP '91 p. 2197.
Fast Algorithm and Implementation of 2-D DCT, Cho & Lee, Tr. CAS v38 p. 297.
A DCT Chip based on a new Structured and Computationally Efficient DCT
  Algorithm, Duhamel, Guillemot & Carlach, ICCAS '90 p. 77.
Trade-offs in the Computation of Mono- and Multi-dimensional DCTs,
  Vetterli, Duhamel & Guillemot, ICASSP '89 p. 999.
Practical Fast 1-D DCT Algorithms with 11 Multiplications,
  Loeffler, Ligtenberg & Moschytz, ICASSP '89 p. 988.
New Scaled DCT Algorithms for Fused Multiply/Add Architectures,
  Linzer & Feig, ICASSP '91 p. 2201.
Fast Algorithms for the 2-D Discrete Cosine Transform, Kamangar & Rao,
  IEEE Tr. Computers, v C-31 p. 899.
Fast 2-D Discrete Cosine Transform, Vetterli, ICASSP '85 p. 1538.
A Two-Dimensional Fast Cosine Transform, Haque, Tr. ASSP v ASSP-33 p. 1532.
Real-Time Parallel and Fully Pipelined 2-D DCT Lattice Structures with
  Application to HDTV Systems, Chiu & Liu, Tr. CAS for Video Tech, v 2 p. 25.
J.F. Blinn, "What's the Deal with the DCT", IEEE Computer Graphics and
  Applications, July 1993, pp.78-83.
A C Hung and TH-Y Meng, "A Comparison of fast DCT algorithms, Multimedia 
  Systems", No. 5 Vol. 2, Dec 1994

For actual implementations, try the JPEG and MPEG software listed
in item 15.

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