Lossless compressionLossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statistical redundancy. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though usually with greatly improved compression rates (and therefore reduced media sizes).
Data compressionIn information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is 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.
Lossy compressionIn 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. The different versions of the photo of the cat on this page show how 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.
Phase modulationPhase modulation (PM) is a modulation pattern for conditioning communication signals for transmission. It encodes a message signal as variations in the instantaneous phase of a carrier wave. Phase modulation is one of the two principal forms of angle modulation, together with frequency modulation. In phase modulation, the instantaneous amplitude of the baseband signal modifies the phase of the carrier signal keeping its amplitude and frequency constant.
Amplitude modulationAmplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the amplitude (signal strength) of the wave is varied in proportion to that of the message signal, such as an audio signal. This technique contrasts with angle modulation, in which either the frequency of the carrier wave is varied, as in frequency modulation, or its phase, as in phase modulation.
Frequency modulationFrequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing. In analog frequency modulation, such as radio broadcasting, of an audio signal representing voice or music, the instantaneous frequency deviation, i.e. the difference between the frequency of the carrier and its center frequency, has a functional relation to the modulating signal amplitude.
Angle modulationAngle modulation is a class of carrier modulation that is used in telecommunications transmission systems. The class comprises frequency modulation (FM) and phase modulation (PM), and is based on altering the frequency or the phase, respectively, of a carrier signal to encode the message signal. This contrasts with varying the amplitude of the carrier, practiced in amplitude modulation (AM) transmission, the earliest of the major modulation methods used widely in early radio broadcasting.
Scheme (mathematics)In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers). Scheme theory was introduced by Alexander Grothendieck in 1960 in his treatise "Éléments de géométrie algébrique"; one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne).
Compression artifactA compression artifact (or artefact) is a noticeable distortion of media (including , audio, and video) caused by the application of lossy compression. Lossy data compression involves discarding some of the media's data so that it becomes small enough to be stored within the desired or transmitted (streamed) within the available bandwidth (known as the data rate or bit rate). If the compressor cannot store enough data in the compressed version, the result is a loss of quality, or introduction of artifacts.
Single-sideband modulationIn radio communications, single-sideband modulation (SSB) or single-sideband suppressed-carrier modulation (SSB-SC) is a type of modulation used to transmit information, such as an audio signal, by radio waves. A refinement of amplitude modulation, it uses transmitter power and bandwidth more efficiently. Amplitude modulation produces an output signal the bandwidth of which is twice the maximum frequency of the original baseband signal.
Group schemeIn mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field. This extra generality allows one to study richer infinitesimal structures, and this can help one to understand and answer questions of arithmetic significance.
Fractal compressionFractal compression is a lossy compression method for s, based on fractals. The method is best suited for textures and natural images, relying on the fact that parts of an image often resemble other parts of the same image. Fractal algorithms convert these parts into mathematical data called "fractal codes" which are used to recreate the encoded image. Iterated function system Fractal image representation may be described mathematically as an iterated function system (IFS).
Fiber product of schemesIn mathematics, specifically in algebraic geometry, the fiber product of schemes is a fundamental construction. It has many interpretations and special cases. For example, the fiber product describes how an algebraic variety over one field determines a variety over a bigger field, or the pullback of a family of varieties, or a fiber of a family of varieties. Base change is a closely related notion. The of schemes is a broad setting for algebraic geometry.
DeflateIn computing, Deflate (stylized as DEFLATE) is a lossless data compression that uses a combination of LZ77 and Huffman coding. It was designed by Phil Katz, for version 2 of his PKZIP archiving tool. Deflate was later specified in RFC 1951 (1996). Katz also designed the original algorithm used to construct Deflate streams. This algorithm was patented as , and assigned to PKWARE, Inc. As stated in the RFC document, an algorithm producing Deflate files was widely thought to be implementable in a manner not covered by patents.
Formal schemeIn mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary scheme, a formal scheme includes infinitesimal data that, in effect, points in a direction off of the scheme. For this reason, formal schemes frequently appear in topics such as deformation theory. But the concept is also used to prove a theorem such as the theorem on formal functions, which is used to deduce theorems of interest for usual schemes.
Dynamic range compressionDynamic 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. Compression is commonly used in sound recording and reproduction, broadcasting, live sound reinforcement and in some instrument amplifiers. A dedicated electronic hardware unit or audio software that applies compression is called a compressor.
Pulse shapingIn electronics and telecommunications, pulse shaping is the process of changing a transmitted pulses' waveform to optimize the signal for its intended purpose or the communication channel. This is often done by limiting the bandwidth of the transmission and filtering the pulses to control intersymbol interference. Pulse shaping is particularly important in RF communication for fitting the signal within a certain frequency band and is typically applied after line coding and modulation.
Hilbert schemeIn algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by . Hironaka's example shows that non-projective varieties need not have Hilbert schemes.
Ultrashort pulseIn optics, an ultrashort pulse, also known as an ultrafast event, is an electromagnetic pulse whose time duration is of the order of a picosecond (10−12 second) or less. Such pulses have a broadband optical spectrum, and can be created by mode-locked oscillators. Amplification of ultrashort pulses almost always requires the technique of chirped pulse amplification, in order to avoid damage to the gain medium of the amplifier. They are characterized by a high peak intensity (or more correctly, irradiance) that usually leads to nonlinear interactions in various materials, including air.
