Added to Favorites

Computing Dictionary

(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.

(1997-03-10)

Explore Dictionary.com

Previous Definition: discrete

Next Definition: discrete fourier transform

Words Near: discrete cosine transform

More from Thesaurus.com

Synonyms and Antonyms for discrete cosine transform

More from Reference.com

Search for articles containing discrete cosine transform

More from Dictionary.com Translator

Translate discrete cosine transform into French

Translate discrete cosine transform into German

Translate discrete cosine transform into Italian

Dictionary.com Word FAQs

Dictionary.com presents 366 FAQs, incorporating some of the frequently asked questions from the past with newer queries.

Related Searches

Nearby Words

Copyright © 2014 Dictionary.com, LLC. All rights reserved.