Editing MPEG-1 (section)

===DCT===
Each 8×8 block is encoded by first applying a ''forward'' [[discrete cosine transform]] (FDCT) and then a quantization process. The FDCT process (by itself) is theoretically lossless, and can be reversed by applying an ''Inverse'' DCT ([[IDCT]]) to reproduce the original values (in the absence of any quantization and rounding errors). In reality, there are some (sometimes large) rounding errors introduced both by quantization in the encoder (as described in the next section) and by IDCT approximation error in the decoder. The minimum allowed accuracy of a decoder IDCT approximation is defined by ISO/IEC 23002-1. (Prior to 2006, it was specified by [[IEEE 1180]]-1990.)

The FDCT process converts the 8×8 block of uncompressed pixel values (brightness or color difference values) into an 8×8 indexed array of ''frequency coefficient'' values. One of these is the (statistically high in variance) "DC coefficient", which represents the average value of the entire 8×8 block. The other 63 coefficients are the statistically smaller "AC coefficients", which have positive or negative values each representing sinusoidal deviations from the flat block value represented by the DC coefficient.

An example of an encoded 8×8 FDCT block: 
:<math>
\begin{bmatrix}
 -415 & -30 & -61 & 27 & 56 & -20 & -2 & 0 \\
 4 & -22 & -61 & 10 & 13 & -7 & -9 & 5 \\
 -47 & 7 & 77 & -25 & -29 & 10 & 5 & -6 \\
 -49 & 12 & 34 & -15 & -10 & 6 & 2 & 2 \\
 12 & -7 & -13 & -4 & -2 & 2 & -3 & 3 \\
 -8 & 3 & 2 & -6 & -2 & 1 & 4 & 2 \\
 -1 & 0 & 0 & -2 & -1 & -3 & 4 & -1 \\
 0 & 0 & -1 & -4 & -1 & 0 & 1 & 2
\end{bmatrix}
</math>

Since the DC coefficient value is statistically correlated from one block to the next, it is compressed using [[Pulse-code modulation|DPCM]] encoding. Only the (smaller) amount of difference between each DC value and the value of the DC coefficient in the block to its left needs to be represented in the final bitstream.

Additionally, the frequency conversion performed by applying the DCT provides a statistical decorrelation function to efficiently concentrate the signal into fewer high-amplitude values prior to applying quantization (see below).