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§¢§à§Ý§î§ê§à§Ö §Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§à §ã§á§Ö§Ü§ä§â§Ñ§Ý§î§ß§í§ç §ã§Ú§ã§ä§Ö§Þ §ã§Ø§Ñ§ä§Ú§ñ §Ú§ã§á§à§Ý§î§Ù§å§ð§ä DCT, §ä§Ñ§Ü §Ü§Ñ§Ü §Ó DCT §Ü§â§å§á§ß§í§Ö §Ü§à§ï§æ§æ§Ú§è§Ú§ß§ä§í §ã§ä§Ñ§â§Ñ§ð§ã§ñ "§Ü§å§é§Ü§à§Ó§Ñ§ä§î§ã§ñ" §Ó §â§Ñ§Û§à§ß§Ö §ß§Ú§Ù§Ü§Ú§ç §é§Ñ§ã§ä§à§ä, §Ñ §Ó §â§Ñ§Û§à§ß§Ö §Ó§í§ã§à§Ü§Ú§ç §é§Ñ§ã§ä§à§ä §Ü§à§ï§æ§æ§Ú§è§Ú§Ö§ß§ä§í §ã§ä§â§Ö§Þ§ñ§ä§ã§ñ §Ü §ß§å§Ý§ð. §¯§Ö §Ù§ß§Ñ§ð §ß§Ú §à§Õ§ß§à§Û §â§Ö§Ñ§Ý§î§ß§à§Û §ã§Ú§ã§ä§Ö§Þ§í §Ô§Õ§Ö §Ò§í §Õ§Ý§ñ §ã§Ø§Ñ§ä§Ú§ñ §Ú§ã§á§à§Ý§î§Ù§à§Ó§Ñ§Ý§à§ã§î DFT, §Õ§Ý§ñ DCT §á§â§Ú§Þ§Ö§â§à§Ó §ã§Ü§à§Ý§î§Ü§à §å§Ô§à§Õ§ß§à.
The discrete cosine transform (DCT) is a frequency transform similar to the discrete Fourier transform (DFT), but using only real numbers. It is equivalent to a DFT of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), where in some variants the input and/or output data are shifted by half a sample. (See below for its properties and applications.)
Applications
The DCT, and in particular the DCT-II, is often used in signal and image processing, especially for lossy data compression, because it has a strong "energy compaction" property: most of the signal information tends to be concentrated in a few low-frequency components of the DCT, approaching the optimal Karhunen-Lo¨¨ve transform for signals based on certain limits of Markov processes.
For example, the DCT is used in JPEG image compression, MJPEG video compression, and MPEG video compression. There, the two-dimensional DCT-II of 8x8 blocks is computed and the results are filtered to discard small (difficult-to-see) components. That is, n is 8 and the DCT-II formula is applied to each row and column of the block. The result is an array in which the top left corner is the DC (zero-frequency) component and lower and rightmore entries represent larger vertical and horizontal spatial frequencies. For the chrominance components, n is 16 but the frequency components beyond the first 8 are discarded.
A related transform, the modified discrete cosine transform (MDCT), is used in AAC, Vorbis, and MP3 audio compression.
DCTs are also widely employed in solving partial differential equations by spectral methods, where the different variants of the DCT correspond to slightly different even/odd boundary conditions at the two ends of the array.
http://en.wikipedia.org/wiki/DCT
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