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Lapped Transform
In signal processing, a lapped transform is a type of linear discrete block transformation where the basis functions of the transformation overlap the block boundaries, yet the number of coefficients overall resulting from a series of overlapping block transforms remains the same as if a non-overlapping block transform had been used. Lapped transforms substantially reduce the blocking artifacts that otherwise occur with block transform coding techniques, in particular those using the discrete cosine transform. The best known example is the modified discrete cosine transform used in the MP3, Vorbis, AAC, and Opus audio codecs. Although the best-known application of lapped transforms has been for audio coding, they have also been used for video and image coding and various other applications. They are used in video coding for coding I-frames in VC-1 and for image coding in the JPEG XR format. More recently, a form of lapped transform has also been used in the development of the Daal ...
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Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomography, seismic signals, Altimeter, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, improve subjective video quality, and to detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was publis ...
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Audio Codec
An audio codec is a device or computer program capable of encoding or decoding a digital data stream (a codec) that encodes or decodes audio. In software, an audio codec is a computer program implementing an algorithm that compresses and decompresses digital audio data according to a given audio file or streaming media audio coding format. The objective of the algorithm is to represent the high-fidelity audio signal with a minimum number of bits while retaining quality. This can effectively reduce the storage space and the bandwidth required for transmission of the stored audio file. Most software codecs are implemented as libraries which interface to one or more multimedia players. Most modern audio compression algorithms are based on modified discrete cosine transform (MDCT) coding and linear predictive coding (LPC). In hardware, audio codec refers to a single device that encodes analog audio as digital signals and decodes digital back into analog. In other words, it contai ...
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Linear Algebra
Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathematics), matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as line (geometry), lines, plane (geometry), planes and rotation (mathematics), rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to Space of functions, function spaces. Linear algebra is also used in most sciences and fields of engineering because it allows mathematical model, modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order a ...
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Digital Signal Processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent Sampling (signal processing), samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor. Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include Audio signal processing, audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for telecommunications, control systems, biomedical engineering, and seismology ...
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Video Coding Format
A video coding format (or sometimes video compression format) is a content representation 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. Video content encoded using a particular video coding format is normally bundled with an audio stream (encoded using an audio coding format) inside a multimedia container format such as AVI, MP4, FLV, RealMedia, or M ...
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Daala (video Codec)
Daala is a video coding format under development by the Xiph.Org Foundation under the lead of Timothy B. Terriberry mainly sponsored by the Mozilla Corporation. Like Theora and Opus, Daala is available free of any royalties and its reference implementation is being developed as free and open-source software. The name is taken from the fictional character of Admiral Natasi Daala from the ''Star Wars'' universe. The reference implementation is written in C and published, together with its source code, as free software under the terms of a BSD-like license. Software patents are being filed for techniques used in and developed for Daala. Those patents are freely licensed to everybody to use for any purpose. However, the patent holders reserve the right to use them to counter patent infringement lawsuits filed by others. Since June 20, 2013, the development is accompanied by a series of sporadically published posts on the underlying technology on the website of the Xiph.Org Foundat ...
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JPEG XR
JPEG XR (JPEG extended range) is an image compression standard for continuous tone photographic images, based on the HD Photo (formerly Windows Media Photo) specifications that Microsoft originally developed and patented. It supports both lossy and lossless compression, and is the preferred image format for Ecma-388 Open XML Paper Specification documents. The format is natively supported by Windows Vista and later as well as Internet Explorer 9, 10 and 11. Third-party support for the format includes Adobe AIR, Affinity Photo, Paint.NET, and Sumatra PDF. History Microsoft first announced Windows Media Photo at WinHEC 2006, and then renamed it to HD Photo in November of that year. In July 2007, the Joint Photographic Experts Group and Microsoft announced HD Photo to be under consideration to become a JPEG standard known as JPEG XR. On 16 March 2009, JPEG XR was given final approval as ITU-T Recommendation T.832 and starting in April 2009, it became available from the I ...
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VC-1
SMPTE 421, informally known as VC-1, is a video coding format. Most of it was initially developed as Microsoft's proprietary video format Windows Media Video 9 in 2003. With some enhancements including the development of a new Advanced Profile, it was officially approved as an SMPTE standard on April 3, 2006. It was primarily marketed as a lower-complexity competitor to the H.264/MPEG-4 AVC standard. After its development, several companies other than Microsoft asserted that they held patents that applied to the technology, including Panasonic, LG Electronics and Samsung Electronics. VC-1 is supported in the now-deprecated Microsoft Silverlight, the briefly-offered HD DVD disc format, and the Blu-ray Disc format. Format VC-1 is an evolution of the conventional block-based motion-compensated hybrid video coding design also found in H.261, MPEG-1 Part 2, H.262/MPEG-2 Part 2, H.263, and MPEG-4 Part 2. It was widely characterized as an alternative to the ITU-T and MPEG video ...
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I-frames
In the field of video compression, a video frame is compressed using different algorithms with different advantages and disadvantages, centered mainly around amount of data compression. These different algorithms for video frames are called picture types or frame types. The three major picture types used in the different video algorithms are I, P and B. They are different in the following characteristics: * I‑frames are the least compressible but don't require other video frames to decode. * P‑frames can use data from previous frames to decompress and are more compressible than I‑frames. * B‑frames can use both previous and forward frames for data reference to get the highest amount of data compression. Summary Three types of ''pictures'' (or frames) are used in video compression: I, P, and B frames. An I‑frame (Intra-frame coding, intra-coded picture) is a complete image, like a JPEG, JPG or BMP file format, BMP image file. A P‑frame (Predicted picture) holds ...
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Opus (codec)
Opus is a lossy audio coding format developed by the Xiph.Org Foundation and standardized by the Internet Engineering Task Force, designed to efficiently code speech and general audio in a single format, while remaining low-latency enough for real-time interactive communication and low-complexity enough for low-end embedded processors. Opus replaces both Vorbis and Speex for new applications. 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. Bitrate, audio bandwidth, complexity, and algorithm can all be adjusted seamlessly in each frame. Opus has the low algorithmic delay (26.5 ms by default) necessary for use as part of a real-time communication link, networked music performances, and live lip sync; by trading off quality or bitrate, the delay can be reduced down to 5 ms. Its delay is exceptionally low compared to competing codecs, which ...
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Linear Transformation
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a . In the case where V = W, a linear map is called a linear endomorphism. Sometimes the term refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily with V = W), or it can be used to emphasize that V is a function space, which is a common convention in functional analysis. Sometimes the term ''linear function'' has the same meaning as ''linear map' ...
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Advanced Audio Coding
Advanced Audio Coding (AAC) is an audio coding standard for lossy digital audio compression. It was developed by Dolby, AT&T, Fraunhofer and Sony, originally as part of the MPEG-2 specification but later improved under MPEG-4.ISO (2006ISO/IEC 13818-7:2006 – Information technology — Generic coding of moving pictures and associated audio information — Part 7: Advanced Audio Coding (AAC), Retrieved on 2009-08-06ISO (2006, Retrieved on 2009-08-06 AAC was designed to be the successor of the MP3 format (MPEG-2 Audio Layer III) and generally achieves higher sound quality than MP3 at the same bit rate. AAC encoded audio files are typically packaged in an MP4 container most commonly using the filename extension .m4a. The basic profile of AAC (both MPEG-4 and MPEG-2) is called AAC-LC (''Low Complexity''). It is widely supported in the industry and has been adopted as the default or standard audio format on products including Apple's iTunes Store, Nintendo's Wii, DSi and ...
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