Discrete cosine transform

DCTiDCTinverse discrete cosine transformFast cosine transform DCTblock codingblock-transformcosinediscrete cosinediscrete cosine transforms (DCT)
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies.wikipedia
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Nasir Ahmed (engineer)

Nasir AhmedN. Ahmed
The DCT, first proposed by Nasir Ahmed in 1972, is the most widely used transformation technique in signal processing and data compression.
He is best known for inventing the discrete cosine transform (DCT) in the early 1970s.

Dolby Digital

Dolby Digital 5.1AC3AC-3
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus).
It is a modification of the discrete cosine transform (DCT) algorithm, which was first proposed by Nasir Ahmed in 1972 and was originally intended for image compression.

Moving Picture Experts Group

MPEGMotion Picture Experts GroupMPEG encoding
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). It is used in image compression standards such as JPEG, and video compression standards such as H.26x, MJPEG, MPEG, DV, Theora and Daala.
All of the MPEG formats listed below use discrete cosine transform (DCT) based lossy video compression algorithms.

Modified discrete cosine transform

MDCTModulated Lapped Transformtime-domain aliasing cancellation
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.
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,

Advanced Audio Coding

AACAAC-LCMPEG-4 AAC
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus).
The discrete cosine transform (DCT), a type of transform coding for lossy compression, was proposed by Nasir Ahmed in 1972, and developed by Ahmed with T. Natarajan and K. R. Rao in 1973, publishing their results in 1974.

Digital video

videodigitaldigitally
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). The wide adoption of DCT compression standards led to the emergence and proliferation of digital media technologies, such as digital images, digital photos, digital video, streaming media, digital television, streaming television, video-on-demand (VOD), digital cinema, high-definition video (HD video), and high-definition television (HDTV).
Practical digital video coding was eventually made possible with the discrete cosine transform (DCT), a form of lossy compression.

Video Coding Experts Group

H.26xVCEGVisual Coding Experts Group (VCEG)
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). It is used in image compression standards such as JPEG, and video compression standards such as H.26x, MJPEG, MPEG, DV, Theora and Daala.
During the late 1980s, a number of companies began experimenting with the much more efficient discrete cosine transform (DCT) compression for video coding, with the CCITT receiving 14 proposals for DCT-based video compression formats, in contrast to a single proposal based on vector quantization (VQ) compression.

Digital television

digitaldigital TVDTV
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). The wide adoption of DCT compression standards led to the emergence and proliferation of digital media technologies, such as digital images, digital photos, digital video, streaming media, digital television, streaming television, video-on-demand (VOD), digital cinema, high-definition video (HD video), and high-definition television (HDTV).
Digital TV became practically feasible in the early 1990s due to a major technological development, discrete cosine transform (DCT) video compression.

Advanced Video Coding

H.264H.264/MPEG-4 AVCMPEG-4 AVC
The integer DCT is used in Advanced Video Coding (AVC), introduced in 2003, and High Efficiency Video Coding (HEVC), introduced in 2013.
Advanced Video Coding (AVC), also referred to as H.264 or MPEG-4 Part 10, Advanced Video Coding (MPEG-4 AVC), is a video compression standard based on block-oriented, motion-compensated integer-DCT coding.

Motion compensation

motion-compensatedmotion estimationmotion compensated
In 1975, John A. Roese and Guner S. Robinson adapted the DCT for inter-frame motion-compensated video coding.
Motion compensation is one of the two key video compression techniques used in video coding standards, along with the discrete cosine transform (DCT).

High Efficiency Video Coding

HEVCH.265H.265/HEVC
The integer DCT is used in Advanced Video Coding (AVC), introduced in 2003, and High Efficiency Video Coding (HEVC), introduced in 2013.
While AVC uses the integer discrete cosine transform (DCT) with 4x4 and 8x8 block sizes, HEVC uses integer DCT and DST transforms with varied block sizes between 4x4 and 32x32.

JPEG 2000

JPEG2000JPEG-2000Motion JPEG 2000
Discrete wavelet transform (DWT) coding is used in the JPEG 2000 standard, developed from 1997 to 2000.
It was developed from 1997 to 2000 by a Joint Photographic Experts Group committee chaired by Touradj Ebrahimi (later the JPEG president), with the intention of superseding their original discrete cosine transform (DCT) based JPEG standard (created in 1992) with a newly designed, wavelet-based method.

Lossy compression

lossylossy data compressioncompressed
Uncompressed digital media as well as lossless compression had impractically high memory and bandwidth requirements, which was significantly reduced by the highly efficient DCT lossy compression technique, capable of achieving data compression ratios from 8:1 to 14:1 for near-studio-quality, up to 100:1 for acceptable-quality content.
The most widely used lossy compression algorithm is the discrete cosine transform (DCT), first published by Nasir Ahmed, T. Natarajan and K. R. Rao in 1974.

Image compression

compressionimagecompressed
He originally intended DCT for image compression.
An important development in image data compression was the discrete cosine transform (DCT), a lossy compression technique first proposed by Nasir Ahmed in 1972.

Discrete sine transform

DSTsinesine transform(s)
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.
The DST is related to the discrete cosine transform (DCT), which is equivalent to a DFT of real and even functions.

K. R. Rao

K.R. Rao
Ahmed developed a practical DCT algorithm with his PhD student T. Natarajan and friend K. R. Rao at the University of Texas at Arlington in 1973, and they found that it was the most efficient algorithm for image compression.
He is credited with the co-invention of discrete cosine transform (DCT), along with Nasir Ahmed and T. Natarajan due to their landmark publication, N. Ahmed, T. Natarajan, and K. R. Rao, "Discrete Cosine Transform", IEEE Transactions on Computers, 90–93, Jan 1974.

Digital media

digital editingdigitalonline media
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). Uncompressed digital media as well as lossless compression had impractically high memory and bandwidth requirements, which was significantly reduced by the highly efficient DCT lossy compression technique, capable of achieving data compression ratios from 8:1 to 14:1 for near-studio-quality, up to 100:1 for acceptable-quality content.
The most important compression technique is the discrete cosine transform (DCT), a lossy compression algorithm that was first proposed as an image compression technique by Nasir Ahmed at the University of Texas in 1972.

Speech coding

speech encodingspeech codecSpeech
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus).
The modified discrete cosine transform (MDCT), a type of discrete cosine transform (DCT) algorithm, was adapted into a speech coding algorithm called LD-MDCT, used for the AAC-LD format introduced in 1999.

Digital audio

digital musicdigitalaudio
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus).
Discrete cosine transform (DCT) coding, a lossy compression method first proposed by Nasir Ahmed in 1972, provided the basis for the modified discrete cosine transform (MDCT), which was developed by J. P. Princen, A. W. Johnson and A. B. Bradley in 1987.

Streaming television

Internet televisionInternet TVInternet
The wide adoption of DCT compression standards led to the emergence and proliferation of digital media technologies, such as digital images, digital photos, digital video, streaming media, digital television, streaming television, video-on-demand (VOD), digital cinema, high-definition video (HD video), and high-definition television (HDTV).
Streaming services were only made possible as a result of two major technological developments: discrete cosine transform (DCT) video compression and asymmetric digital subscriber line (ADSL) data transmission.

High Efficiency Image File Format

HEIFHigh Efficiency Image FormatHEIC
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus).
Like JPEG, HEIF is based on the discrete cosine transform (DCT), a form of lossy compression.

Digital cinema

digital projectiondigital6K
The wide adoption of DCT compression standards led to the emergence and proliferation of digital media technologies, such as digital images, digital photos, digital video, streaming media, digital television, streaming television, video-on-demand (VOD), digital cinema, high-definition video (HD video), and high-definition television (HDTV).
It is a modification of the discrete cosine transform (DCT) algorithm, which was first proposed by Nasir Ahmed in 1972 and was originally intended for image compression.

Siren (codec)

SirenSiren 14Siren Codec
It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG, H.26x and Vorbis), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus).
The algorithm is based on transform coding technology, using a modulated lapped transform (MLT), a type of discrete cosine transform (DCT) or modified discrete cosine transform (MDCT).

Clenshaw–Curtis quadrature

Clenshaw–Curtis integration
DCTs are also closely related to Chebyshev polynomials, and fast DCT algorithms (below) are used in Chebyshev approximation of arbitrary functions by series of Chebyshev polynomials, for example in Clenshaw–Curtis quadrature.
Equivalently, they employ a change of variables and use a discrete cosine transform (DCT) approximation for the cosine series.

DV

MiniDVDVCAMDVCPRO
It is used in image compression standards such as JPEG, and video compression standards such as H.26x, MJPEG, MPEG, DV, Theora and Daala.
An intraframe video compression scheme is used to compress video on a frame-by-frame basis with the discrete cosine transform (DCT).