Discrete cosine transform in the context of "MP3"

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⭐ Core Definition: Discrete cosine transform

A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as JPEG and HEIF), digital video (such as MPEG and H.26x), 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). DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations.

A DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier series coefficients of a periodically and symmetrically extended sequence whereas DFTs are related to Fourier series coefficients of only periodically extended sequences. DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input or output data are shifted by half a sample.

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Discrete cosine transform in the context of JPEG

JPEG (/ˈpɛɡ/ JAY-peg, short for Joint Photographic Experts Group and sometimes retroactively referred to as JPEG 1) is a commonly used method of lossy compression for digital images, particularly for those images produced by digital photography. The degree of compression can be adjusted, allowing a selectable trade off between storage size and image quality. JPEG typically achieves 10:1 compression with noticeable, but widely agreed to be acceptable perceptible loss in image quality. Since its introduction in 1992, JPEG has been the most widely used image compression standard in the world, and the most widely used digital image format, with several billion JPEG images produced every day as of 2015.

The Joint Photographic Experts Group created the standard in 1992, based on the discrete cosine transform (DCT) algorithm. JPEG was largely responsible for the proliferation of digital images and digital photos across the Internet and later social media. JPEG compression is used in a number of image file formats. JPEG/Exif is the most common image format used by digital cameras and other photographic image capture devices; along with JPEG/JFIF, it is the most common format for storing and transmitting photographic images on the World Wide Web. These format variations are often not distinguished and are simply called JPEG.

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Discrete cosine transform in the context of Lossy compression

In information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size for storing, handling, and transmitting content. Higher degrees of approximation create coarser images as more details are removed. This is opposed to lossless data compression (reversible data compression) which does not degrade the data. The amount of data reduction possible using lossy compression is much higher than using lossless techniques.

Well-designed lossy compression technology often reduces file sizes significantly before degradation is noticed by the end-user. Even when noticeable by the user, further data reduction may be desirable (e.g., for real-time communication or to reduce transmission times or storage needs). 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.

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Discrete cosine transform in the context of Video coding format

A video coding format (or sometimes video compression format) is an encoded format of digital video content, such as in a data file or bitstream. It typically uses a standardized video compression algorithm, most commonly based on discrete cosine transform (DCT) coding and motion compensation. A computer software or hardware component that compresses or decompresses a specific video coding format is a video codec.

Some video coding formats are documented by a detailed technical specification document known as a video coding specification. Some such specifications are written and approved by standardization organizations as technical standards, and are thus known as a video coding standard. There are de facto standards and formal standards.

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Discrete cosine transform in the context of N. Ahmed

Nasir Ahmed (born 1940) is an American electrical engineer and computer scientist. He is Professor Emeritus of Electrical and Computer Engineering at University of New Mexico (UNM). He is best known for inventing the discrete cosine transform (DCT) in the early 1970s. The DCT is the most widely used data compression transformation, the basis for most digital media standards (image, video and audio) and commonly used in digital signal processing. He also described the discrete sine transform (DST), which is related to the DCT.

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Discrete cosine transform in the context of K. R. Rao

Kamisetty Ramamohan Rao (1931 – 2021) was an Indian-American electrical engineer. He was a professor of Electrical Engineering at the University of Texas at Arlington (UT Arlington). Academically known as K. R. Rao, he is credited with the co-invention of discrete cosine transform (DCT), along with Nasir Ahmed and T. Natarajan due to their landmark publication, Discrete Cosine Transform.

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Discrete cosine transform in the context of Dolby Digital

Dolby Digital, originally synonymous with Dolby AC-3 (see below), is the name for a family of audio compression technologies developed by Dolby Laboratories. Called Dolby Stereo Digital until 1995, it uses lossy compression (except for Dolby TrueHD). The first use of Dolby Digital was to provide digital sound in cinemas from 35 mm film prints. It has since also been used for TV broadcast, radio broadcast via satellite, digital video streaming, DVDs, Blu-ray discs and game consoles.

Dolby AC-3 was the original version of the Dolby Digital codec. The basis of the Dolby AC-3 multi-channel audio coding standard is the modified discrete cosine transform (MDCT), a lossy audio compression algorithm. It is a modification of the discrete cosine transform (DCT) algorithm, which was proposed by Nasir Ahmed in 1972 for image compression. The DCT was adapted into the MDCT by J.P. Princen, A.W. Johnson and Alan B. Bradley at the University of Surrey in 1987.

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Discrete cosine transform in the context of H.264/MPEG-4 AVC

Advanced Video Coding (AVC), also referred to as H.264 or MPEG-4 Part 10, is a video compression standard based on block-oriented, motion-compensated coding. It is by far the most commonly used format for the recording, compression, and distribution of video content, used by 79% of video industry developers as of December 2024. It supports a maximum resolution of 8K UHD.

The intent of the H.264/AVC project was to create a standard capable of providing good video quality at substantially lower bit rates than previous standards (i.e., half or less the bit rate of MPEG-2, H.263, or MPEG-4 Part 2), without increasing the complexity of design so much that it would be impractical or excessively expensive to implement. This was achieved with features such as a reduced-complexity integer discrete cosine transform (integer DCT), variable block-size segmentation, and multi-picture inter-picture prediction. An additional goal was to provide enough flexibility to allow the standard to be applied to a wide variety of applications on a wide variety of networks and systems, including low and high bit rates, low and high resolution video, broadcast, DVD storage, RTP/IP packet networks, and ITU-T multimedia telephony systems. The H.264 standard can be viewed as a "family of standards" composed of a number of different profiles, although its "High profile" is by far the most commonly used format. A specific decoder decodes at least one, but not necessarily all profiles. The standard describes the format of the encoded data and how the data is decoded, but it does not specify algorithms for encoding—that is left open as a matter for encoder designers to select for themselves, and a wide variety of encoding schemes have been developed. H.264 is typically used for lossy compression, although it is also possible to create truly lossless-coded regions within lossy-coded pictures or to support rare use cases for which the entire encoding is lossless.

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