The discrete cosine transform, abbreviated DCT, expresses a finite real sequence using sampled cosine functions. The commonly used type-II
DCT of 
,
..., 
is
 |
where 
,
..., 
,
,
and 
for 
.
With this normalization the transformation is orthogonal,
and its inverse is
 |
The DCT is closely related to the discrete Fourier transform of an even extension of the sequence and is widely used for data compression.
