A generalized fast algorithm for n-D discrete cosine transform and its application to motion picture coding

Zhishun Wang; Zhenya He; Cairong Zou; J. D.Z. Chen

doi:10.1109/82.769810

A generalized fast algorithm for n-D discrete cosine transform and its application to motion picture coding

Zhishun Wang, Zhenya He, Cairong Zou, J. D.Z. Chen

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

In this paper, a generalized fast computational algorithm for the n -dimensional discrete cosine transform (DCT) of length N = 2^m (m > 2) is presented. The developed algorithm is proved and its efficiency is evaluated theoretically. The theoretical results show that compared with the conventional method of computing the one-dimensional along n directions, the number of multiplications needed by our algorithm is only 1/n of that required by the conventional method; for the total number of additions, the latter is a bit more when N < 8 and much fewer when N > 16 than the former. To validate the proposed algorithm, we take the case when n -3 as an example and apply it to motion-picture coding. The results show that our method is superior to MPEG-2 in speed and coding performance. The algorithm is clearly described and it is easy to make a computer program for implementation.

Original language	English (US)
Pages (from-to)	617-627
Number of pages	11
Journal	IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing
Volume	46
Issue number	5
DOIs	https://doi.org/10.1109/82.769810
State	Published - 1999
Externally published	Yes

Keywords

Discrete cosine transform (dct)
Fast algorithm
MPEG
Motion picture coding
Multidimensional signal processing

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/82.769810

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title = "A generalized fast algorithm for n-D discrete cosine transform and its application to motion picture coding",

abstract = "In this paper, a generalized fast computational algorithm for the n -dimensional discrete cosine transform (DCT) of length N = 2m (m > 2) is presented. The developed algorithm is proved and its efficiency is evaluated theoretically. The theoretical results show that compared with the conventional method of computing the one-dimensional along n directions, the number of multiplications needed by our algorithm is only 1/n of that required by the conventional method; for the total number of additions, the latter is a bit more when N < 8 and much fewer when N > 16 than the former. To validate the proposed algorithm, we take the case when n -3 as an example and apply it to motion-picture coding. The results show that our method is superior to MPEG-2 in speed and coding performance. The algorithm is clearly described and it is easy to make a computer program for implementation.",

keywords = "Discrete cosine transform (dct), Fast algorithm, MPEG, Motion picture coding, Multidimensional signal processing",

author = "Zhishun Wang and Zhenya He and Cairong Zou and Chen, {J. D.Z.}",

note = "Funding Information: Manuscript received March 16, 1998; revised October 26, 1998. This work was supported by the Climbing Program, National Key Project for Fundamental Research in China, under Grant NSC 92097. This paper was recommended by Associate Editor J. Astola. Z. Wang and J. D. Z. Chen are with Lynn Institute for Healthcare Research, Oklahoma City, OK 73112 USA. Z. He and C. Zou are with the Radio Engineering Department, Southeast University, Nanjing 210096, China. Publisher Item Identifier S 1057-7130(99)03788-X.",

year = "1999",

doi = "10.1109/82.769810",

language = "English (US)",

volume = "46",

pages = "617--627",

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T1 - A generalized fast algorithm for n-D discrete cosine transform and its application to motion picture coding

AU - Wang, Zhishun

AU - He, Zhenya

AU - Zou, Cairong

AU - Chen, J. D.Z.

N1 - Funding Information: Manuscript received March 16, 1998; revised October 26, 1998. This work was supported by the Climbing Program, National Key Project for Fundamental Research in China, under Grant NSC 92097. This paper was recommended by Associate Editor J. Astola. Z. Wang and J. D. Z. Chen are with Lynn Institute for Healthcare Research, Oklahoma City, OK 73112 USA. Z. He and C. Zou are with the Radio Engineering Department, Southeast University, Nanjing 210096, China. Publisher Item Identifier S 1057-7130(99)03788-X.

PY - 1999

Y1 - 1999

N2 - In this paper, a generalized fast computational algorithm for the n -dimensional discrete cosine transform (DCT) of length N = 2m (m > 2) is presented. The developed algorithm is proved and its efficiency is evaluated theoretically. The theoretical results show that compared with the conventional method of computing the one-dimensional along n directions, the number of multiplications needed by our algorithm is only 1/n of that required by the conventional method; for the total number of additions, the latter is a bit more when N < 8 and much fewer when N > 16 than the former. To validate the proposed algorithm, we take the case when n -3 as an example and apply it to motion-picture coding. The results show that our method is superior to MPEG-2 in speed and coding performance. The algorithm is clearly described and it is easy to make a computer program for implementation.

AB - In this paper, a generalized fast computational algorithm for the n -dimensional discrete cosine transform (DCT) of length N = 2m (m > 2) is presented. The developed algorithm is proved and its efficiency is evaluated theoretically. The theoretical results show that compared with the conventional method of computing the one-dimensional along n directions, the number of multiplications needed by our algorithm is only 1/n of that required by the conventional method; for the total number of additions, the latter is a bit more when N < 8 and much fewer when N > 16 than the former. To validate the proposed algorithm, we take the case when n -3 as an example and apply it to motion-picture coding. The results show that our method is superior to MPEG-2 in speed and coding performance. The algorithm is clearly described and it is easy to make a computer program for implementation.

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KW - Motion picture coding

KW - Multidimensional signal processing

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A generalized fast algorithm for n-D discrete cosine transform and its application to motion picture coding

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