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Pyramid Vector Quantization
Pyramid vector quantization (PVQ) is a method used in audio and video codecs to quantize and transmit unit vectors, i.e. vectors whose magnitudes are known to the decoder but whose directions are unknown. PVQ may also be used as part of a gain/shape quantization scheme, whereby the magnitude and direction of a vector are quantized separately from each other. PVQ was initially described in 1986 in the paper "A Pyramid Vector Quantizer" by Thomas R. Fischer. One caveat of PVQ is that it operates under the taxicab distance (L1-norm). Conversion to/from the more familiar Euclidean distance (L2-norm) is possible via vector projection, though results in a less uniform distribution of quantization points (the poles of the Euclidean ''n''-sphere become denser than non-poles). No efficient algorithm for the ideal (i.e., uniform) vector quantization of the Euclidean ''n''-sphere is known as of 2010. This non-uniformity can be reduced by applying deformation like coordinate-wise power befo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Codec
A codec is a device or computer program that encodes or decodes a data stream or signal. ''Codec'' is a portmanteau of coder/decoder. In electronic communications, an endec is a device that acts as both an encoder and a decoder on a signal or data stream, and hence is a type of codec. ''Endec'' is a portmanteau of encoder/decoder. A coder or encoder encodes a data stream or a signal for transmission or storage, possibly in encrypted form, and the decoder function reverses the encoding for playback or editing. Codecs are used in videoconferencing, streaming media, and video editing applications. History In the mid-20th century, a codec was a device that coded analog signals into digital form using pulse-code modulation (PCM). Later, the name was also applied to software for converting between digital signal formats, including companding functions. Examples An audio codec converts analog audio signals into digital signals for transmission or encodes them for storage. A receiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daala
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 Founda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Quantization
Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. It was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms. The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. This is why VQ is suitable for lossy data compression. It can also be used for lossy data correction and density estimation. Vector quantization is based on the competitive learning paradigm, so it is closely related to the self-organizing map model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat"). The term ''direction vector'', commonly denoted as d, is used to describe a unit vector being used to represent spatial direction and relative direction. 2D spatial directions are numerically equivalent to points on the unit circle and spatial directions in 3D are equivalent to a point on the unit sphere. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e., :\mathbf = \frac where , u, is the norm (or length) of u. The term ''normalized vector'' is sometimes used as a synonym for ''unit vector''. Unit vectors are often chosen to form the basis of a vector space, and every vector in the space may be written as a linear combination of unit vectors. Orthogonal coordinates Cartesian coordinates Unit vectors may be us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set-builder Notation
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy. Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension. Sets defined by enumeration A set can be described directly by enumerating all of its elements between curly brackets, as in the following two examples: * \ is the set containing the four numbers 3, 7, 15, and 31, and nothing else. * \=\ is the set containing , , and , and nothing else (there is no order among the elements of a set). This is sometimes called the "roster method" for specifying a set. When it is desired to denote a set that contains elements from a regular sequence, an ellipses notation may be employed, as shown in the next examples: * \ is the set of integers between 1 and 100 inclusive. * \ is the set of natura ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
L1-norm
In mathematics, the spaces are function spaces defined using a natural generalization of the -norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue , although according to the Bourbaki group they were first introduced by Frigyes Riesz . spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role in the mathematical analysis of measure and probability spaces, Lebesgue spaces are used also in the theoretical discussion of problems in physics, statistics, economics, finance, engineering, and other disciplines. Applications Statistics In statistics, measures of central tendency and statistical dispersion, such as the mean, median, and standard deviation, are defined in terms of metrics, and measures of central tendency can be characterized as solutions to variational problems. In penalized regression, "L1 penalty" and "L2 penalty" refer to penali ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), and For example, the absolute value of 3 and the absolute value of −3 is The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts. Terminology and notation In 1806, Jean-Robert Argand introduced the term ''module'', meaning ''unit of measure'' in French, specifically for the ''complex'' absolute value,Oxford English Dictionary, Draft Revision, June 2008 an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Quantization
Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. It was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms. The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. This is why VQ is suitable for lossy data compression. It can also be used for lossy data correction and density estimation. Vector quantization is based on the competitive learning paradigm, so it is closely related to the self-organizing map model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Opus (audio Format)
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, and several blind listening tests have ranked it higher-quality than any other standard audio format at any given bitrate until transparency is reached, including MP3, AAC, and HE-AAC. 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, networke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantization (signal Processing)
Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms. The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer. Example For example, rounding a real number x to the nearest integer value forms a very basic type of quantizer – a ''uniform'' one. A typical (''mid-tread'') uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
