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Quantization (signal processing)

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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. [1]

103 relations: Allen Gersho, Analog-to-digital converter, Arithmetic coding, Automatic gain control, Bell Labs, Bell System Technical Journal, Bernard Widrow, Beta encoder, Biology, Bit numbering, Centroid, Chemistry, Claude Shannon, Closed-form expression, Communications system, Companding, Conceptual model, Convex hull, Countable set, Data binning, Data compression, Deadband, Decibel, Digital signal processing, Discrete time and continuous time, Discretization, Discretization error, Dither, DNA, Dynamic range compression, Electron, Electronics, Entropy (information theory), Entropy encoding, Exponential distribution, Finite set, Floor and ceiling functions, Gary Sullivan (engineer), Generalized normal distribution, IEEE Communications Magazine, IEEE Transactions on Information Theory, Institute of Mathematical Statistics, John Wiley & Sons, K-means clustering, Lagrange multiplier, Laplace distribution, Limit cycle, Linde–Buzo–Gray algorithm, Lloyd's algorithm, London Mathematical Society, ..., Lossy compression, Mean squared error, Molecule, Nariman Farvardin, Noise gate, Noise shaping, Nonlinear system, Normal distribution, Optics, Photon, Physics, Planck's law, Posterization, Probability density function, Proceedings of the IEEE, Pseudorandomness, Pulse-code modulation, Quantile, Quantization (signal processing), Random variable, Rate–distortion theory, Real number, Regression dilution, Robert M. Gray, Root mean square, Round-off error, Rounding, S&P Global, Sampling (signal processing), Sawtooth wave, Sign function, Signal-to-quantization-noise ratio, Sine wave, Spectral density, Springer Science+Business Media, Squelch, Stair riser, Stairs, Standard deviation, Stochastic, Subroutine, Toby Berger, Triangle wave, Truncation, Uncountable set, Uniform distribution (continuous), Variable-length code, Vector quantization, White noise, William Fleetwood Sheppard, 16-bit, 24-bit, 8-bit. Expand index (53 more) »

Allen Gersho

Allen Gersho is a professor emeritus at UCSB who made significant contributions in the area of signal compression and speech coding.

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Analog-to-digital converter

In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal.

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Arithmetic coding

Arithmetic coding is a form of entropy encoding used in lossless data compression.

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Automatic gain control

Automatic gain control (AGC), also called automatic volume control (AVC), is a closed-loop feedback regulating circuit in an amplifier or chain of amplifiers, the purpose of which is to maintain a suitable signal amplitude at its output, despite variation of the signal amplitude at the input.

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Bell Labs

Nokia Bell Labs (formerly named AT&T Bell Laboratories, Bell Telephone Laboratories and Bell Labs) is an American research and scientific development company, owned by Finnish company Nokia.

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Bell System Technical Journal

The Bell System Technical Journal was a periodical publication by the American Telephone and Telegraph Company (AT&T) in New York devoted to the scientific and engineering aspects of electrical communication.

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Bernard Widrow

Bernard Widrow (born December 24, 1929) is a U.S. professor of electrical engineering at Stanford University.

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Beta encoder

A beta encoder is an analog-to-digital conversion (A/D) system in which a real number in the unit interval is represented by a finite representation of a sequence in base beta, with beta being a real number between 1 and 2.

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Biology is the natural science that studies life and living organisms, including their physical structure, chemical composition, function, development and evolution.

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Bit numbering

In computing, bit numbering (or sometimes bit endianness) is the convention used to identify the bit positions in a binary number or a container for such a value.

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In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the shape.

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Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.

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Claude Shannon

Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as "the father of information theory".

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Closed-form expression

In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.

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Communications system

In telecommunication, a communications system is a collection of individual communications networks, transmission systems, relay stations, tributary stations, and data terminal equipment (DTE) usually capable of interconnection and interoperation to form an integrated whole.

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In telecommunication and signal processing companding (occasionally called compansion) is a method of mitigating the detrimental effects of a channel with limited dynamic range.

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Conceptual model

A conceptual model is a representation of a system, made of the composition of concepts which are used to help people know, understand, or simulate a subject the model represents.

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Convex hull

In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.

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Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

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Data binning

Data binning or bucketing is a data pre-processing technique used to reduce the effects of minor observation errors.

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Data compression

In signal processing, data compression, source coding, or bit-rate reduction involves encoding information using fewer bits than the original representation.

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A deadband (sometimes called a neutral zone or dead zone) is a band of input values in the domain of a transfer function in a control system or signal processing system where the output is zero (the output is 'dead' - no action occurs).

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The decibel (symbol: dB) is a unit of measurement used to express the ratio of one value of a physical property to another on a logarithmic scale.

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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.

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Discrete time and continuous time

In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.

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In mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts.

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Discretization error

In numerical analysis, computational physics, and simulation, discretization error is the error resulting from the fact that a function of a continuous variable is represented in the computer by a finite number of evaluations, for example, on a lattice.

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Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images.

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Deoxyribonucleic acid (DNA) is a thread-like chain of nucleotides carrying the genetic instructions used in the growth, development, functioning and reproduction of all known living organisms and many viruses.

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Dynamic range compression

Dynamic range compression (DRC) or simply compression is an audio signal processing operation that reduces the volume of loud sounds or amplifies quiet sounds thus reducing or compressing an audio signal's dynamic range.

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The electron is a subatomic particle, symbol or, whose electric charge is negative one elementary charge.

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Electronics is the discipline dealing with the development and application of devices and systems involving the flow of electrons in a vacuum, in gaseous media, and in semiconductors.

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Entropy (information theory)

Information entropy is the average rate at which information is produced by a stochastic source of data.

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Entropy encoding

In information theory an entropy encoding is a lossless data compression scheme that is independent of the specific characteristics of the medium.

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Exponential distribution

No description.

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Finite set

In mathematics, a finite set is a set that has a finite number of elements.

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Floor and ceiling functions

In mathematics and computer science, the floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x, denoted \operatorname(x).

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Gary Sullivan (engineer)

Gary Joseph Sullivan (born 1960) is an American electrical engineer who led the development of the H.264/MPEG-4 AVC and HEVC video coding standards and created the DirectX Video Acceleration (DXVA) API/DDI video decoding feature of the Microsoft Windows operating system.

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Generalized normal distribution

The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line.

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IEEE Communications Magazine

The IEEE Communications Magazine is a monthly magazine published by the IEEE Communications Society dealing with all areas of communications including light-wave telecommunications, high-speed data communications, personal communications systems (PCS), ISDN, and more.

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IEEE Transactions on Information Theory

IEEE Transactions on Information Theory is a monthly peer-reviewed scientific journal published by the IEEE Information Theory Society.

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Institute of Mathematical Statistics

The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability.

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John Wiley & Sons

John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.

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K-means clustering

k-means clustering is a method of vector quantization, originally from signal processing, that is popular for cluster analysis in data mining.

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Lagrange multiplier

In mathematical optimization, the method of Lagrange multipliers (named after Joseph-Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).

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Laplace distribution

In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.

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Limit cycle

In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity.

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Linde–Buzo–Gray algorithm

The Linde–Buzo–Gray algorithm (introduced by Yoseph Linde, Andrés Buzo and Robert M. Gray in 1980) is a vector quantization algorithm to derive a good codebook.

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Lloyd's algorithm

In computer science and electrical engineering, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces and partitions of these subsets into well-shaped and uniformly sized convex cells.

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London Mathematical Society

The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)).

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Lossy compression

In information technology, lossy compression or irreversible compression is the class of data encoding methods that uses inexact approximations and partial data discarding to represent the content.

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Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and what is estimated.

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A molecule is an electrically neutral group of two or more atoms held together by chemical bonds.

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Nariman Farvardin

Nariman Farvardin (born July 15, 1956) is an Iranian-American engineer and educator, currently serving as President of Stevens Institute of Technology, Hoboken, New Jersey.

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Noise gate

A noise gate or gate is an electronic device or software that is used to control the volume of an audio signal.

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Noise shaping

Noise shaping is a technique typically used in digital audio, image, and video processing, usually in combination with dithering, as part of the process of quantization or bit-depth reduction of a digital signal.

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Nonlinear system

In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.

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Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

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Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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The photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force (even when static via virtual particles).

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Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Planck's law

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T. The law is named after Max Planck, who proposed it in 1900.

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Posterization or posterisation of an image entails conversion of a continuous gradation of tone to several regions of fewer tones, with abrupt changes from one tone to another.

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Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

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Proceedings of the IEEE

The Proceedings of the IEEE is a monthly peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers (IEEE).

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A pseudorandom process is a process that appears to be random but is not.

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Pulse-code modulation

Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals.

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In statistics and probability quantiles are cut points dividing the range of a probability distribution into contiguous intervals with equal probabilities, or dividing the observations in a sample in the same way.

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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.

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Random variable

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.

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Rate–distortion theory

Rate–distortion theory is a major branch of information theory which provides the theoretical foundations for lossy data compression; it addresses the problem of determining the minimal number of bits per symbol, as measured by the rate R, that should be communicated over a channel, so that the source (input signal) can be approximately reconstructed at the receiver (output signal) without exceeding a given distortion D.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Regression dilution

Regression dilution, also known as regression attenuation, is the biasing of the regression slope towards zero (the underestimation of its absolute value), caused by errors in the independent variable.

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Robert M. Gray

Robert M. Gray (born November 1, 1943) is an American information theorist, and the Alcatel-Lucent Professor of Electrical Engineering at Stanford University in Palo Alto, California.

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Root mean square

In statistics and its applications, the root mean square (abbreviated RMS or rms) is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers).

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Round-off error

A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.

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Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing $ with $, or the fraction 312/937 with 1/3, or the expression with.

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S&P Global

S&P Global Inc. (prior to April 2016 McGraw Hill Financial, Inc., and prior to 2013 McGraw Hill Companies) is an American publicly traded corporation headquartered in New York City.

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Sampling (signal processing)

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal.

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Sawtooth wave

The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform.

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Sign function

In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.

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Signal-to-quantization-noise ratio

Signal-to-Quantization-Noise Ratio (SQNR or SNqR) is widely used quality measure in analysing digitizing schemes such as PCM (pulse code modulation) and multimedia codecs.

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Sine wave

A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation.

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Spectral density

The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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In telecommunications, squelch is a circuit function that acts to suppress the audio (or video) output of a receiver in the absence of a sufficiently strong desired input signal.

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Stair riser

A stair riser is the near-vertical element in a set of stairs, forming the space between one step and the next.

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A stairway, staircase, stairwell, flight of stairs, or simply stairs is a construction designed to bridge a large vertical distance by dividing it into smaller vertical distances, called steps.

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Standard deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

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The word stochastic is an adjective in English that describes something that was randomly determined.

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In computer programming, a subroutine is a sequence of program instructions that performs a specific task, packaged as a unit.

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Toby Berger

Toby Berger (born September 4, 1940) is a noted American information theorist.

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Triangle wave

A triangle wave is a non-sinusoidal waveform named for its triangular shape.

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In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.

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Uncountable set

In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable.

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Uniform distribution (continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

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Variable-length code

In coding theory a variable-length code is a code which maps source symbols to a variable number of bits.

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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.

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White noise

In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.

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William Fleetwood Sheppard

William Fleetwood Sheppard FRSE LLM (20 November 1863 – 12 October 1936) Australian-British civil servant, mathematician and statistician remembered for his work in finite differences, interpolation and statistical theory, known in particular for the eponymous Sheppard's corrections.

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16-bit microcomputers are computers in which 16-bit microprocessors were the norm.

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Notable 24-bit machines include the CDC 924 – a 24-bit version of the CDC 1604, CDC lower 3000 series, SDS 930 and SDS 940, the ICT 1900 series, and the Datacraft minicomputers/Harris H series.

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8-bit is also a generation of microcomputers in which 8-bit microprocessors were the norm.

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8-bit sample, Adaptive Quantization, Adaptive quantization, Dead-zone quantizer, Q-noise, Quantisation (signal processing), Quantisation error, Quantisation noise, Quantiser, Quantization (sound processing), Quantization distortion, Quantization error, Quantization error model, Quantization noise, Quantized signal, Quantizer, Quantizing noise, Scalar quantization, Signal quantization.


[1] https://en.wikipedia.org/wiki/Quantization_(signal_processing)

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