conditions, while the DCT basis functions are the irreducible representations of the dihedral group, making the DCT natural for signals with symmetric (even) boundary conditions.

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. This was the original DCT as first proposed by Ahmed. Its inverse, the type-III DCT, is correspondingly often called simply the inverse DCT or the