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Thursday, February 16, 2006

MDCT

Modified Descrete Cosine Transform >>

The modified discrete cosine transform (MDCT) is a Fourier-related 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. Thus, an MDCT is employed in MP3, AC-3, Ogg Vorbis, and AAC for audio compression, for example.

(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.)

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. ATRAC uses stacked quadrature mirror filters (QMF) followed by an MDCT.

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