Discrete Cosine Transform


Created by Mauricio Alvarez
Last update: 06.11.2003

Fast 1D-DCT  Algorithms


Algorithm
Year
Mult.-1D*
Add/Sub-1D*
Mult-2D **
Add/Sub-2D**
Implementation
Reference 1D-DCT
N. Ahmed, T. Natarjan and K. R. Rao. [1]
1974
64
64
1024
1024
MOM
W.-H. Chen H. Smith and S.C. Fralick. [2]
1977
16
26
224
416

W.-H. Chen H. Smith and S.C. Fralick. Fast
1977
13
29
176
464
Scalar MPEG encoding
Altivec [14]
Z. Wang. [3]
1984
13
29



B. Lee. [4]
1984
12
29



M. Vetterli and  N. Nussbaumer. [5]
1984
12
29



N. Suheiro and M. Hatori. [6]
1986
12
29



H. S. Hou. [7]
1987
12
29



Y. Arai, T. Agui and M. Nakajima. [8]
1988
13
29
144
464
MMX/SSE [15]
SSE2[17]
Loeffler, Ligtengerb and Moschytz. [9]
1988
12
32
224
416

Loeffler, Ligtengerb and Moschytz. Fast.
1989
11
29
176
464
Scalar JPEG encoding
MMX.[16]
Artieri and Colavin. [10]
1990






*Operation per 8x8 element 1D-DCT

Fast 2D-DCT  Algorithms

Algorithm
Year
Mult-2D.**
Add/Sub-2D**
Implementation
Reference 2D DCT

4096
4096

Kamangar and Rao. [12] 1982 128 430
]Cho and Lee (2D).[11] 1993 96
466
Feig and Winograd[13]
1992
94
454


** Operations per 8x8 2D-DCT

References