|
This overlapping, in addition to the energy-compaction qualities of the DCT, makes the MDCT especially attractive for signal compression applications, since it helps to avoid [[compression artifact|artifacts]] stemming from the block boundaries. As a result of these advantages, the MDCT is employed in most modern lossy audio formats, including [[MP3]], [[Dolby AC-3|AC-3]], [[Vorbis]], [[Windows Media Audio]], [[ATRAC]], [[cook codec|Cook]], [[advanced audio coding|AAC]], [[Opus_(audio_format)|Opus]], and [[LDAC_(codec)|LDAC]].
The [[discrete cosine transform]] (DCT) was introducedfirst proposed by [[N. Ahmed|Nasir Ahmed]] in 1972,<ref name="Ahmed">{{cite journal |last=Ahmed |first=Nasir |author-link=N. Ahmed |title=How I Came Up With the Discrete Cosine Transform |journal=[[Digital Signal Processing (journal)|Digital Signal Processing]] |date=January 1991 |volume=1 |issue=1 |pages=4–5 |doi=10.1016/1051-2004(91)90086-Z |url=https://www.scribd.com/doc/52879771/DCT-History-How-I-Came-Up-with-the-Discrete-Cosine-Transform}}</ref> and demonstrated by Ahmed with T. Natarajan and [[K. R. Rao]] in 1974.<ref name="pubDCT">{{Citation |first=Nasir |last=Ahmed |author1-link=N. Ahmed |first2=T. |last2=Natarajan |first3=K. R. |last3=Rao |title=Discrete Cosine Transform |journal=IEEE Transactions on Computers |date=January 1974 |volume=C-23 |issue=1 |pages=90–93 |doi=10.1109/T-C.1974.223784}}</ref> The MDCT was later proposed by J. P. Princen, A. W. Johnson and A.Alan B. Bradley at the [[University of Surrey]] in 1987,<ref>{{cite journal |last1=Princen |first1=J. P. Princen,|last2=Johnson |first2=A. W. Johnson|last3=Bradley und A.|first3=Alan B. Bradley: ''|title=Subband/transformTransform coding using filter bank designs based on time ___domain aliasing cancellation'', IEEE|journal=ICASSP Proc'87. Intl.IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2161–2164, |date=1987. Initial|volume=12 description|pages=2161–2164 of what is now called the MDCT|doi=10.1109/ICASSP.1987.1169405}}</ref> following earlier work by Princen and Bradley (1986)<ref>John P. Princen, Alan B. Bradley: ''Analysis/synthesis filter bank design based on time ___domain aliasing cancellation'', IEEE Trans. Acoust. Speech Signal Processing, ''ASSP-34'' (5), 1153–1161, 1986. Described a precursor to the MDCT using a combination of discrete cosine and sine transforms.</ref> 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.)
In MP3, the MDCT is not applied to the audio signal directly, but rather to the output of a 32-band [[polyphase quadrature filter]] (PQF) bank. The output of this MDCT is postprocessed by an alias reduction formula to reduce the typical aliasing of the PQF filter bank. Such a combination of a filter bank with an MDCT is called a ''hybrid'' filter bank or a ''subband'' MDCT. AAC, on the other hand, normally uses a pure MDCT; only the (rarely used) [[MPEG-4 AAC-SSR]] variant (by [[Sony]]) uses a four-band PQF bank followed by an MDCT. Similar to MP3, [[ATRAC]] uses stacked [[quadrature mirror filter]]s (QMF) followed by an MDCT.
|
