Discrete Cosine Transform
lastmod 2018-08-17created 2014-09-014 edits
The discrete cosine transform, DCT (discrete cosine transform), is a transform similar to the discrete Fourier transform (DFT). It is also called isan yeohyeon byeonhwan (離散餘弦變換), its Sino-Korean name. Compared to the DFT, it is nearly the same, except that it operates on real-valued even functions of twice the length. This is because the Fourier transform of a real-valued even function is also a real-valued even function. There are eight variants, such as shifting the input/output data by half a sample, of which four are widely used.
The most widely used variant DCT algorithm is the type-II DCT, which is often simply called "the DCT". Its inverse is the type-III DCT, which is likewise simply called "the inverse DCT" or "IDCT".
There are two transforms related to the DCT. The discrete sine transform (DST) is equivalent to the DFT of a real-valued odd function, and the modified discrete cosine transform (MDCT), the other one, uses overlapping data.