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- Q2877 subject Q7013138.
- Q2877 subject Q8380265.
- Q2877 subject Q8470619.
- Q2877 abstract "A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio (e.g. MP3) and images (e.g. JPEG) (where small high-frequency components can be discarded), to spectral methods for the numerical solution of partial differential equations. The use of cosine rather than sine functions is critical for compression, since it turns out (as described below) that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions.In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. DCTs are equivalent to DFTs 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. There are eight standard DCT variants, of which four are common.The most common variant of discrete cosine transform is the type-II DCT, which is often called simply "the DCT". Its inverse, the type-III DCT, is correspondingly often called simply "the inverse DCT" or "the IDCT". Two related transforms are the discrete sine transform (DST), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data.".
- Q2877 thumbnail Example_dft_dct.svg?width=300.
- Q2877 wikiPageExternalLink summary.php?id=e71-e_11_1095.
- Q2877 wikiPageExternalLink www.fftw.org.
- Q2877 wikiPageExternalLink pg=624.
- Q2877 wikiPageExternalLink 184410889..
- Q2877 wikiPageExternalLink fftw-paper-ieee.pdf.
- Q2877 wikiPageExternalLink ltfat.sourceforge.net.
- Q2877 wikiPageExternalLink DCT_TR802.pdf.
- Q2877 wikiPageExternalLink fft.html..
- Q2877 wikiPageExternalLink IDCT.
- Q2877 wikiPageExternalLink DCT-History-How-I-Came-Up-with-the-Discrete-Cosine-Transform.
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- Q2877 wikiPageWikiLink Q7013138.
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- Q2877 wikiPageWikiLink Q8380265.
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- Q2877 comment "A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio (e.g. MP3) and images (e.g. JPEG) (where small high-frequency components can be discarded), to spectral methods for the numerical solution of partial differential equations.".
- Q2877 label "Discrete cosine transform".
- Q2877 depiction Example_dft_dct.svg.