Modified discrete cosine transform

MDCTModulated Lapped Transformtime-domain aliasing cancellationMDCTs
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.wikipedia
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Discrete cosine transform

DCTiDCTinverse discrete cosine transform
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, The discrete cosine transform (DCT) was first proposed by Nasir Ahmed in 1972, and demonstrated by Ahmed with T. Natarajan and K. R. Rao in 1974.
Two related transforms are the discrete sine transform (DST), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data.

Dolby Digital

Dolby Digital 5.1AC3AC-3
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
Originally named Dolby Stereo Digital until 1994, except for Dolby TrueHD, the audio compression is lossy, based on the modified discrete cosine transform (MDCT) algorithm.

MP3

.mp3MP3 downloadMP3 files
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
The remaining audio information is then recorded in a space-efficient manner, using MDCT and FFT algorithms.

Lapped transform

discrete cosine transform with overlapping blocks
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,
The best known example is the modified discrete cosine transform used in the MP3, Vorbis, AAC, and Opus audio codecs.

Advanced Audio Coding

AACAAC-LCMPEG-4 AAC
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
AAC uses a purely modified discrete cosine transform (MDCT) algorithm, giving it higher compression efficiency than MP3, which uses a hybrid coding algorithm that is part MDCT and part FFT.

Vorbis

Ogg VorbisOGGaoTuV
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
Vorbis had been shown to perform significantly better than many other lossy audio formats in the past in that it produced smaller files at equivalent or higher quality while retaining computational complexity comparable to other MDCT formats such as AAC or Windows Media Audio.

Windows Media Audio

WMAWMA LosslessWMA Pro
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
Fundamentally, WMA is a transform coder based on modified discrete cosine transform (MDCT), somewhat similar to AAC, Cook and Vorbis.

Speech coding

speech encodingspeech codecSpeech
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
The most widely used speech coding technique in mobile telephony is linear predictive coding (LPC), while the most widely used in VoIP applications are the LPC and modified discrete cosine transform (MDCT) techniques.

Adaptive Transform Acoustic Coding

ATRACATRAC3ATRAC3plus
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
Like ATRAC1 and MP3, ATRAC3 is also a hybrid subband-MDCT encoder, but with several differences.

Compression artifact

artifactscompression artifactsmosquito noise
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.
Lossy audio formats typically involve the use of a time/frequency domain transform, such as a modified discrete cosine transform.

Opus (audio format)

OpusOpus audio format.opus
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
Opus combines the speech-oriented LPC-based SILK algorithm and the lower-latency MDCT-based CELT algorithm, switching between or combining them as needed for maximal efficiency.

Lossy compression

lossylossy data compressioncompressed
As a result of these advantages, the MDCT is the most widely used lossy compression technique in audio data compression.

Cook Codec

CookCook'' codecRealAudio Gecko
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
It is a pure transform codec based on the modified discrete cosine transform with a single block size.

AAC-LD

AAC-ELDAAC LD
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
AAC-LD uses a version of the modified discrete cosine transform (MDCT) audio coding technique called the LD-MDCT.

MPEG-H 3D Audio

3D Audio
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
Audio is encoded using an improved modified discrete cosine transform (MDCT) algorithm.

G.722.1

G.722
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
It uses a modified discrete cosine transform (MDCT) audio data compression algorithm.

CELT

Constrained Energy Lapped Transform
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
CELT is a transform codec based on the modified discrete cosine transform (MDCT) and concepts from CELP (with a code book for excitation, but in the frequency domain).

Polyphase quadrature filter

polyphasedPQF
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.
Similar to the MDCT time domain alias cancellation the aliasing of polyphase quadrature filters is canceled by neighbouring sub-bands, i.e. signals are typically stored in two sub-bands.

LDAC (codec)

LDACLDAC codec
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
LDAC is a lossy codec, which employs a hybrid coding scheme based on the Modified discrete cosine transform to provide more efficient data compression.

Dolby AC-4

It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
AC-4 uses an improved modified discrete cosine transform (MDCT) audio coding algorithm.

Nasir Ahmed (engineer)

Nasir AhmedN. Ahmed
The discrete cosine transform (DCT) was first proposed by Nasir Ahmed in 1972, and demonstrated by Ahmed with T. Natarajan and K. R. Rao in 1974.
A DCT variant, the modified discrete cosine transform (MDCT), is used in modern audio compression formats such as MP3, Advanced Audio Coding (AAC), and Vorbis (OGG).

G.729.1

It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
The G.729.1 algorithm is based on a three-stage coding structure: embedded code-excited linear prediction (CELP) coding of the lower band (50–4000 Hz), parametric coding of the higher band (4000–7000 Hz) by Time-Domain Bandwidth Extension (TDBWE), and enhancement of the full band (50–7000 Hz) by a predictive transform coding technique referred to as time-domain aliasing cancellation (TDAC) or modified discrete cosine transform (MDCT) coding.

K. R. Rao

K.R. Rao
The discrete cosine transform (DCT) was first proposed by Nasir Ahmed in 1972, and demonstrated by Ahmed with T. Natarajan and K. R. Rao in 1974.

Short-time Fourier transform

STFTresolution issues of the short-time Fourier transformshort time Fourier transform
See also the modified discrete cosine transform (MDCT), which is also a Fourier-related transform that uses overlapping windows.

Audio coding format

audio codingaudio coding standardaudio compression format
It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), LDAC, Dolby AC-4, MPEG-H 3D Audio, as well as speech coding standards such as AAC-LD (LD-MDCT), G.722.1, G.729.1, CELT, and Opus.
The most widely used audio coding formats are MP3 and Advanced Audio Coding (AAC), both of which are lossy formats based on modified discrete cosine transform (MDCT) and perceptual coding algorithms.