Printer Friendly
Dictionary, Encyclopedia and Thesaurus - The Free Dictionary
3,895,356,969 visitors served.
forum Join the Word of the Day Mailing List For webmasters
?
Dictionary/
thesaurus
Medical
dictionary
Legal
dictionary
Financial
dictionary
Acronyms
 
Idioms
Encyclopedia
Wikipedia
encyclopedia
?

discrete cosine transform
(redirected from DCT (math))

   Also found in: Wikipedia 0.03 sec.
(mathematics)discrete cosine transform - (DCT) A technique for expressing a waveform as a weighted sum of cosines.

The DCT is central to many kinds of signal processing, especially video compression.

Given data A(i), where i is an integer in the range 0 to N-1, the forward DCT (which would be used e.g. by an encoder) is:

B(k) = sum A(i) cos((pi k/N) (2 i + 1)/2) i=0 to N-1

B(k) is defined for all values of the frequency-space variable k, but we only care about integer k in the range 0 to N-1. The inverse DCT (which would be used e.g. by a decoder) is:

AA(i)= sum B(k) (2-delta(k-0)) cos((pi k/N)(2 i + 1)/2) k=0 to N-1

where delta(k) is the Kronecker delta.

The main difference between this and a discrete Fourier transform (DFT) is that the DFT traditionally assumes that the data A(i) is periodically continued with a period of N, whereas the DCT assumes that the data is continued with its mirror image, then periodically continued with a period of 2N.

Mathematically, this transform pair is exact, i.e. AA(i) == A(i), resulting in lossless coding; only when some of the coefficients are approximated does compression occur.

There exist fast DCT algorithms in analogy to the Fast Fourier Transform.


Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content.
?Page tools
Printer friendly
Cite / link
Feedback
Mentioned in?   Encyclopedia browser?   Full browser?
No references found
 
 
 
Encyclopedia
?

Terms of Use | Privacy policy | Feedback | Advertise with Us | Copyright © 2012 Farlex, Inc.
Disclaimer
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.