Understanding the Modified Discrete Cosine Transform (MDCT) 🎶

The modified discrete cosine transform is a lapped transform based on the type-IV discrete cosine transform, 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, AAC, and Opus.
The MDCT was proposed by Princen, Johnson, and Bradley in 1987, following earlier work by Princen and Bradley to develop the MDCT's underlying principle of time-domain aliasing cancellation, described below.


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