discrete cosine transform
The discrete cosine transforms (DCT) are a family of transforms closely related to the discrete sine transform and the discrete Fourier transform. The DCT-II is the most commonly used form and plays an important role in coding signals and images , e.g. in the widely used standard JPEG compression. The discrete cosine transform was first introduced by Ahmed, Natarajan, and Rao . Later Wang and Hunt  introduced the set of variants.
The DCT is included in many mathematical packages, such as Matlab, Mathematica and GNU Octave.
The DCT-I is its own inverse.
The inverse of DCT-II is DCT-III.
The inverse of DCT-III is DCT-II.
The DCT-IV is its own inverse.
The DCT-V is its own inverse.
The inverse of DCT-VI is DCT-VII.
The inverse of DCT-VII is DCT-VI.
The DCT-VIII is its own inverse.
2 Two-dimensional DCT
The DCT in two dimensions is simply the one-dimensional transform computed in each row and each column. For example, the DCT-II of a matrix is given by
- 1 This entry is based on content from The Data Analysis Briefbook (http://rkb.home.cern.ch/rkb/titleA.htmlhttp://rkb.home.cern.ch/rkb/titleA.html)
- 2 A.K. Jain, Fundamentals of Digital Image Processing, Prentice Hall, 1989.
- 3 Xuancheng Shao, Steven G. Johnson. Type-II/III DCT/DST algorithms with reduced number of arithmetic operations. 2007.
- 4 Markus Päuschel, José M. F. Mouray. The algebraic approach to the discrete cosine and sine transforms and their fast algorithms. 2006.
- 5 N. Ahmed, T. Natarajan, and K. R. Rao. Discrete Cosine Transform, IEEE Trans. on Computers, C-23. 1974.
- 6 Z. Wang and B. Hunt, The Discrete W Transform, Applied Mathematics and Computation, 16. 1985.
|Title||discrete cosine transform|
|Date of creation||2013-03-22 12:11:24|
|Last modified on||2013-03-22 12:11:24|
|Last modified by||stitch (17269)|
|Synonym||discrete trigonometric transforms|