# discrete cosine transform

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## discrete cosine transform

(mathematics)
(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.
References in periodicals archive ?
The Integer Modified Discrete Cosine Transform (Int-MDCT) approximates the MDCT while producing integer output values.
There are many transforms can be used for images watermarking based on frequency domain (FD), such as continuous wavelet transform (CWT), discrete cosine transform (DCT), short time Fourier transform (STFT), discrete wavelet transforms (DWT), Fourier transform, and combinations of DCT and DWT.
Jen, "A new array architecture for prime-length discrete cosine transform," IEEE Transactions on Signal Processing, vol.
The dictionary based on discrete wavelet transform basis function with MOD and KSVD produced accurate result as compared to dictionary based on discrete cosine transform basis function.
i], then A can be diagonalized by the discrete cosine transform (DCT) [15, Theorem 3.
Discrete cosine transform (DCT) is a general orthogonal transform for digital image processing and signal processing, with such advantages, as high compression ratio, small bit error rate, good information integration ability and good synthetic effect of calculation complexity.
In this paper, we reported a hardware implementation scheme and results of a Loeffler algorithm based 2-D discrete cosine transform codec.
There are several signal transformations which have been considered in the literature, they include the Discrete Fourier Transform [4], Discrete Cosine Transform [5] and Discrete Wavelet Transform [6].
The log of this spectrum is then taken and the discrete cosine transform is applied [2].
Although discrete cosine transform techniques (DCT), discrete Fourier transform (DFT) and discreet wavelet transform (DWT) etc.
PowerPressed reportedly uses a compression technology based on Discrete Cosine Transform (DCT), which delivers much more effective compression than binary compression can achieve, allowing PowerPressed to reduce the file by up to 95%.
Kowalczuk reprinted paper VLSI for digital television (Proceedings of the IEEE, July 1995) in which a complete digital television system is considered, other papers are on architecture design issues for discrete cosine transform algorithms and wavelets transform for video communications.

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