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The modified discrete cosine transform (MDCT) is a lapped transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being ''lapped'': it is designed to be performed on consecutive blocks of a larger dataset, where subsequent blocks are overlapped so that the last half of one block coincides with the first half of the next block. 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 artifacts stemming from the block boundaries. As a result of these advantages, the MDCT is employed in most modern lossy audio formats, including MP3, AC-3, Vorbis, Windows Media Audio, ATRAC, Cook, and AAC. The MDCT was proposed by Princen, Johnson, and Bradley〔J. P. Princen, A. W. Johnson und A. B. Bradley: ''Subband/transform coding using filter bank designs based on time domain aliasing cancellation'', IEEE Proc. Intl. Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2161–2164, 1987. Initial description of what is now called the MDCT.〕 in 1987, following earlier (1986) work by Princen and Bradley〔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.〕 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 filters (QMF) followed by an MDCT. == Definition == As a lapped transform, the MDCT is a bit unusual compared to other Fourier-related transforms in that it has half as many outputs as inputs (instead of the same number). In particular, it is a linear function (where R denotes the set of real numbers). The 2''N'' real numbers ''x''0, ..., ''x''2''N''-1 are transformed into the ''N'' real numbers ''X''0, ..., ''X''''N''-1 according to the formula: : (The normalization coefficient in front of this transform, here unity, is an arbitrary convention and differs between treatments. Only the product of the normalizations of the MDCT and the IMDCT, below, is constrained.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Modified discrete cosine transform」の詳細全文を読む スポンサード リンク
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