In principle, there are actually four additional types of discrete sine transform ( Martucci, 1994 ), corresponding to real-odd DFTs of logically odd order, which have factors of " N " + 1 / 2 in the denominators of the sine arguments.
12.
Two related transforms are the discrete sine transform ( DST ), which is equivalent to a DFT of real and " odd " functions, and the modified discrete cosine transform ( MDCT ), which is based on a DCT of " overlapping " data.
13.
The MDCT was proposed by Princen, Johnson, and Bradley in 1987, following earlier ( 1986 ) work by Princen and Bradley to develop the MDCT's underlying principle of "'time-domain aliasing cancellation "'( TDAC ), described below . ( There also exists an analogous transform, the MDST, based on the discrete sine transform, as well as other, rarely used, forms of the MDCT based on different types of DCT or DCT / DST combinations .)
