Modified discrete cosine transform

The modified discrete cosine transform (MDCT) is a transform based on the type-IV <a href="/facts/Discrete_cosine_transform/gPpDhPwP">discrete cosine transform</a> (DCT-IV), with the additional property of being <a href="/facts/Lapped_transform/BafAb414">lapped</a>: it is designed to be performed on consecutive blocks of a larger <a href="/facts/Dataset/eDvegUTK">dataset</a>, 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 <a href="/facts/Compression_artifact/7DhxoVAv">artifacts</a> stemming from the block boundaries. As a result of these advantages, the MDCT is the most widely used <a href="/facts/Lossy_compression/jHW7DDv3">lossy compression</a> technique in <a href="/facts/Audio_data_compression/gMFuY4FT">audio data compression</a>. It is employed in most modern <a href="/facts/Audio_coding_standards/qHAhppfD">audio coding standards</a>, including <a href="/facts/MP3/yrBpxUSD">MP3</a>, <a href="/facts/Dolby_Digital/58JfURnU">Dolby Digital</a> (AC-3), <a href="/facts/Vorbis/rqJDTF0T">Vorbis</a> (Ogg), <a href="/facts/Windows_Media_Audio/s5zePro7">Windows Media Audio</a> (WMA), <a href="/facts/ATRAC/kD9psz23">ATRAC</a>, <a href="/facts/Cook_codec/Pun19XWQ">Cook</a>, <a href="/facts/Advanced_Audio_Coding/VAG9NpI4">Advanced Audio Coding</a> (AAC), <a href="/facts/High-Definition_Coding/28rXJDWn">High-Definition Coding</a> (HDC), <a href="/facts/LDAC_(codec)/IMFHz8ux">LDAC</a>, <a href="/facts/Dolby_AC-4/FXj0MW2d">Dolby AC-4</a>, and <a href="/facts/MPEG-H_3D_Audio/tPvIwD8f">MPEG-H 3D Audio</a>, as well as <a href="/facts/Speech_coding/xs5gvMXq">speech coding</a> standards such as <a href="/facts/AAC-LD/VndVLu7F">AAC-LD</a> (LD-MDCT), <a href="/facts/G.722.1/0K92h1Eg">G.722.1</a>, <a href="/facts/G.729.1/7azV3ohe">G.729.1</a>, <a href="/facts/CELT/52Wt9cbu">CELT</a>, and <a href="/facts/Opus_(audio_format)/VP4KuGre">Opus</a>.
The <a href="/facts/Discrete_cosine_transform/gPpDhPwP">discrete cosine transform</a> (DCT) was first proposed by <a href="/facts/N._Ahmed/LImldyWe">Nasir Ahmed</a> in 1972, and demonstrated by Ahmed with T. Natarajan and <a href="/facts/K._R._Rao/DwrVrQ6u">K. R. Rao</a> in 1974. The MDCT was later proposed by John P. Princen, A.W. Johnson and Alan B. Bradley at the <a href="/facts/University_of_Surrey/cJdmCo4Y">University of Surrey</a> in 1987, following earlier work by Princen and Bradley (1986) 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 <a href="/facts/Discrete_sine_transform/GRtd90kB">discrete sine transform</a>, 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 <a href="/facts/Polyphase_quadrature_filter/4BBPIMPf">polyphase quadrature filter</a> (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) <a href="/facts/MPEG-4_AAC-SSR/PIqK5dk9">MPEG-4 AAC-SSR</a> variant (by <a href="/facts/Sony/7x4tCtBd">Sony</a>) uses a four-band PQF bank followed by an MDCT. Similar to MP3, <a href="/facts/ATRAC/kD9psz23">ATRAC</a> uses stacked <a href="/facts/Quadrature_mirror_filter/YVVNJapY">quadrature mirror filters</a> (QMF) followed by an MDCT.

Modified discrete cosine transform open-in-new

Modified discrete cosine transform