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Audio Data Compression
In signal processing , DATA COMPRESSION, SOURCE CODING, or BIT-RATE REDUCTION involves encoding information using fewer bits than the original representation. Compression can be either lossy or lossless . Lossless compression reduces bits by identifying and eliminating statistical redundancy . No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information. The process of reducing the size of a data file is referred to as data compression. In the context of data transmission , it is called source coding (encoding done at the source of the data before it is stored or transmitted) in opposition to channel coding. Compression is useful because it reduces resources required to store and transmit data. Computational resources are consumed in the compression process and, usually, in the reversal of the process (decompression)
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Sequitur Algorithm
SEQUITUR (or NEVILL-MANNING ALGORITHM) is a recursive algorithm developed by Craig Nevill-Manning and Ian H. Witten in 1997 that infers a hierarchical structure (context-free grammar ) from a sequence of discrete symbols. The algorithm operates in linear space and time. It can be used in data compression software applications. CONTENTS* 1 Constraints * 1.1 Digram uniqueness * 1.2 Rule utility * 2 Method summary * 3 See also * 4 References * 5 External links CONSTRAINTSThe sequitur algorithm constructs a grammar by substituting repeating phrases in the given sequence with new rules and therefore produces a concise representation of the sequence. For example, if the sequence is S→abcab, the algorithm will produce S→AcA, A→ab. While scanning the input sequence, the algorithm follows two constraints for generating its grammar efficiently: DIGRAM UNIQUENESS and RULE UTILITY
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Probabilistic Model
A STATISTICAL MODEL is a class of mathematical model , which embodies a set of assumptions concerning the generation of some sample data , and similar data from a larger population . A statistical model represents, often in considerably idealized form, the data-generating process. The assumptions embodied by a statistical model describe a set of probability distributions , some of which are assumed to adequately approximate the distribution from which a particular data set is sampled. The probability distributions inherent in statistical models are what distinguishes statistical models from other, non-statistical, mathematical models. A statistical model is usually specified by mathematical equations that relate one or more random variables and possibly other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen )
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Arithmetic Coding
ARITHMETIC CODING is a form of entropy encoding used in lossless data compression . Normally, a string of characters such as the words "hello there" is represented using a fixed number of bits per character, as in the ASCII code. When a string is converted to arithmetic encoding, frequently used characters will be stored with fewer bits and not-so-frequently occurring characters will be stored with more bits, resulting in fewer bits used in total. Arithmetic coding differs from other forms of entropy encoding, such as Huffman coding , in that rather than separating the input into component symbols and replacing each with a code, arithmetic coding encodes the entire message into a single number, an arbitrary-precision fraction q where 0.0 ≤ q < 1.0. It represents the current information as a range, defined by two numbers. Recent Asymmetric Numeral Systems family of entropy coders allows for faster implementations thanks to directly operating on a single natural number representing the current information. An arithmetic coding example assuming a fixed probability distribution of three Symbols "A", "B", and "C". Probability of "A" is 50%, probability of "B" is 33% and probability of "C" is 17%. Furthermore we assume that the recursion depth is known in each step. In step one we code "B" which is inside the interval Encoding the message "WIKI" with arithmetic coding 1. The letter frequencies are found. 2. The interval In the simplest case, the probability of each symbol occurring is equal
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Finite-state Machine
A FINITE-STATE MACHINE (FSM) or FINITE-STATE AUTOMATON (FSA, plural: automata), FINITE AUTOMATON, or simply a STATE MACHINE, is a mathematical model of computation . It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some external inputs; the change from one state to another is called a transition. An FSM is defined by a list of its states, its initial state, and the conditions for each transition
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Grammar-based Codes
GRAMMAR-BASED CODES or GRAMMAR-BASED COMPRESSION are compression algorithms based on the idea of constructing a context-free grammar (CFG) for the string to be compressed. Examples include universal lossless data compression algorithms. To compress a data sequence x = x 1 x n {displaystyle x=x_{1}cdots x_{n}} , a grammar-based code transforms x {displaystyle x} into a context-free grammar G {displaystyle G} . The problem of finding a smallest grammar for an input sequence is known to be NP-hard, , so many grammar-transform algorithms are proposed from theoretical and practical viewpoints. Generally, the produced grammar G {displaystyle G} is further compressed by statistical encoders like arithmetic coding . CONTENTS * 1 Examples and characteristics * 2 Practical algorithms * 3 See also * 4 References * 5 External links EXAMPLES AND CHARACTERISTICSThe class of grammar-based codes is very broad
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Burrows–Wheeler Transform
The BURROWS–WHEELER TRANSFORM (BWT, also called BLOCK-SORTING COMPRESSION) rearranges a character string into runs of similar characters. This is useful for compression, since it tends to be easy to compress a string that has runs of repeated characters by techniques such as move-to-front transform and run-length encoding . More importantly, the transformation is REVERSIBLE, without needing to store any additional data. The BWT is thus a "free" method of improving the efficiency of text compression algorithms, costing only some extra computation. CONTENTS * 1 Description * 2 Example * 3 Explanation * 4 Optimization * 5 Bijective variant * 6 Dynamic Burrows–Wheeler transform * 7 Sample implementation * 8 BWT in bioinformatics * 9 References * 10 External links DESCRIPTIONThe Burrows–Wheeler transform is an algorithm used to prepare data for use with data compression techniques such as bzip2
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Source Code
In computing , SOURCE CODE is any collection of computer instructions , possibly with comments , written using a HUMAN-READABLE programming language , usually as ordinary text . The source code of a program is specially designed to facilitate the work of computer programmers , who specify the actions to be performed by a computer mostly by writing source code. The source code is often transformed by an assembler or compiler into binary machine code understood by the computer. The machine code might then be stored for execution at a later time. Alternatively, source code may be interpreted and thus immediately executed. Most application software is distributed in a form that includes only executable files. If the source code were included it would be useful to a user , programmer or a system administrator , any of whom might wish to study or modify the program
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LZX (algorithm)
LZX is an LZ77 family compression algorithm . It is also the name of a file archiver with the same name. Both were invented by Jonathan Forbes and Tomi Poutanen
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Probabilistic Algorithm
A RANDOMIZED ALGORITHM is an algorithm that employs a degree of randomness as part of its logic. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random bits. Formally, the algorithm's performance will be a random variable determined by the random bits; thus either the running time, or the output (or both) are random variables. One has to distinguish between algorithms that use the random input so that they always terminate with the correct answer, but where the expected running time is finite (Las Vegas algorithms , example of which is Quicksort ), and algorithms which have a chance of producing an incorrect result (Monte Carlo algorithms , example of which is Monte Carlo algorithm for MFAS ) or fail to produce a result either by signaling a failure or failing to terminate
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Prediction By Partial Matching
PREDICTION BY PARTIAL MATCHING (PPM) is an adaptive statistical data compression technique based on context modeling and prediction . PPM models use a set of previous symbols in the uncompressed symbol stream to predict the next symbol in the stream. PPM algorithms can also be used to cluster data into predicted groupings in cluster analysis . CONTENTS * 1 Theory * 2 Implementation * 3 See also * 4 Sources * 5 References * 6 External links THEORYPredictions are usually reduced to symbol rankings . Each symbol (a letter, bit or any other amount of data) is ranked before it is compressed and, the ranking system determines the corresponding codeword (and therefore the compression rate). In many compression algorithms, the ranking is equivalent to probablity mass function estimation. Given the previous letters (or given a context), each symbol is assigned with a probablity
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Probability Distribution
In probability theory and statistics , a PROBABILITY DISTRIBUTION is a mathematical function that, stated in simple terms, can be thought of as providing the probabilities of occurrence of different possible outcomes in an experiment . For instance, if the random variable X is used to denote the outcome of a coin toss ('the experiment'), then the probability distribution of X would take the value 0.5 for X = heads {displaystyle X={text{heads}}} , and 0.5 for X = tails {displaystyle X={text{tails}}} (assuming the coin is fair). In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events . Examples of random phenomena can include the results of an experiment or survey . A probability distribution is defined in terms of an underlying sample space , which is the set of all possible outcomes of the random phenomenon being observed
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JPEG
JPEG
JPEG
(/ˈdʒeɪpɛɡ/ JAY-peg ) 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 tradeoff between storage size and image quality . JPEG
JPEG
typically achieves 10:1 compression with little perceptible loss in image quality. JPEG
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
World Wide Web
. These format variations are often not distinguished, and are simply called JPEG
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Psychoacoustics
PSYCHOACOUSTICS is the scientific study of sound perception . More specifically, it is the branch of science studying the psychological and physiological responses associated with sound (including noise , speech and music ). It can be further categorized as a branch of psychophysics . Psychoacoustics
Psychoacoustics
received its name from a field within psychology—i.e., recognition science—which deals with all kinds of human perceptions. It is an interdisciplinary field of many areas, including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science
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Digital Camera
A DIGITAL CAMERA or DIGICAM is a camera that produces images that can be stored in digital memory , displayed on a screen and printed on physical media. Most cameras produced today are digital, and digital cameras are incorporated into many devices ranging from PDAs and mobile phones (called camera phones ) to vehicles. Digital and movie cameras share an optical system, typically using a lens with a variable diaphragm to focus light onto an image pickup device. The diaphragm and shutter admit the correct amount of light to the imager, just as with film but the image pickup device is electronic rather than chemical. However, unlike film cameras, digital cameras can display images on a screen immediately after being recorded, and store and delete images from memory . Many digital cameras can also record moving videos with sound . Some digital cameras can crop and stitch pictures and perform other elementary image editing
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DVD
DVD
DVD
(an abbreviation of "DIGITAL VIDEO DISC" or "DIGITAL VERSATILE DISC" ) is a digital optical disc storage format invented and developed by Philips
Philips
and Sony
Sony
in 1995. The medium can store any kind of digital data and is widely used for software and other computer files as well as video programs watched using DVD
DVD
players . DVDs offer higher storage capacity than compact discs while having the same dimensions. Prerecorded DVDs are mass-produced using molding machines that physically stamp data onto the DVD. Such discs are a form of DVD-ROM because data can only be read and not written or erased. Blank recordable DVD
DVD
discs ( DVD-R and DVD+R ) can be recorded once using a DVD recorder and then function as a DVD-ROM
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