Side
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 ofboundary conditions.
The DCT is used in JPEG image compression, MJPEG, MPEG, DV, Daala,
and Theora video compression. There, the two-dimensional DCT-II of blocks
are computed and the results are quantized and entropy coded. In this case, is
typically 8 and the DCT-II formula is applied to each row and column of the block.
The result is an 8 × 8 transform coefficient array in which the element (top-
annaabi.ee 
