Noise (electronics)In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects. In particular, noise is inherent in physics and central to thermodynamics. Any conductor with electrical resistance will generate thermal noise inherently. The final elimination of thermal noise in electronics can only be achieved cryogenically, and even then quantum noise would remain inherent. Electronic noise is a common component of noise in signal processing.
Topological data analysisIn applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools.
Noise reductionNoise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio. All signal processing devices, both analog and digital, have traits that make them susceptible to noise.
Colors of noiseIn audio engineering, electronics, physics, and many other fields, the color of noise or noise spectrum refers to the power spectrum of a noise signal (a signal produced by a stochastic process). Different colors of noise have significantly different properties. For example, as audio signals they will sound differently to human ears, and as they will have a visibly different texture. Therefore, each application typically requires noise of a specific color.
Noise controlNoise control or noise mitigation is a set of strategies to reduce noise pollution or to reduce the impact of that noise, whether outdoors or indoors. The main areas of noise mitigation or abatement are: transportation noise control, architectural design, urban planning through zoning codes, and occupational noise control. Roadway noise and aircraft noise are the most pervasive sources of environmental noise.
Persistence moduleA persistence module is a mathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological features of an object across a range of scale parameters. A persistence module often consists of a collection of homology groups (or vector spaces if using field coefficients) corresponding to a filtration of topological spaces, and a collection of linear maps induced by the inclusions of the filtration.
Pseudometric spaceIn mathematics, a pseudometric space is a generalization of a metric space in which the distance between two distinct points can be zero. Pseudometric spaces were introduced by Đuro Kurepa in 1934. In the same way as every normed space is a metric space, every seminormed space is a pseudometric space. Because of this analogy the term semimetric space (which has a different meaning in topology) is sometimes used as a synonym, especially in functional analysis. When a topology is generated using a family of pseudometrics, the space is called a gauge space.
Persistent homologySee homology for an introduction to the notation. Persistent homology is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected over a wide range of spatial scales and are deemed more likely to represent true features of the underlying space rather than artifacts of sampling, noise, or particular choice of parameters. To find the persistent homology of a space, the space must first be represented as a simplicial complex.
Pink noisePink noise, noise or fractal noise is a signal or process with a frequency spectrum such that the power spectral density (power per frequency interval) is inversely proportional to the frequency of the signal. In pink noise, each octave interval (halving or doubling in frequency) carries an equal amount of noise energy. Pink noise sounds like a waterfall. It is often used to tune loudspeaker systems in professional audio. Pink noise is one of the most commonly observed signals in biological systems.
Shot noiseShot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics shot noise originates from the discrete nature of electric charge. Shot noise also occurs in photon counting in optical devices, where shot noise is associated with the particle nature of light. In a statistical experiment such as tossing a fair coin and counting the occurrences of heads and tails, the numbers of heads and tails after many throws will differ by only a tiny percentage, while after only a few throws outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot.
Signal-to-noise ratioSignal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. SNR is an important parameter that affects the performance and quality of systems that process or transmit signals, such as communication systems, audio systems, radar systems, imaging systems, and data acquisition systems.
NoiseNoise is unwanted sound considered unpleasant, loud, or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arises when the brain receives and perceives a sound. Acoustic noise is any sound in the acoustic domain, either deliberate (e.g., music or speech) or unintended. In contrast, noise in electronics may not be audible to the human ear and may require instruments for detection.
Uniform spaceIn the mathematical field of topology, a uniform space is a topological space with additional structure that is used to define uniform properties, such as completeness, uniform continuity and uniform convergence. Uniform spaces generalize metric spaces and topological groups, but the concept is designed to formulate the weakest axioms needed for most proofs in analysis. In addition to the usual properties of a topological structure, in a uniform space one formalizes the notions of relative closeness and closeness of points.
Metrizable topological vector spaceIn functional analysis and related areas of mathematics, a metrizable (resp. pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric). An LM-space is an inductive limit of a sequence of locally convex metrizable TVS.
Trivial topologyIn topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such spaces are commonly called indiscrete, anti-discrete, concrete or codiscrete. Intuitively, this has the consequence that all points of the space are "lumped together" and cannot be distinguished by topological means. Every indiscrete space is a pseudometric space in which the distance between any two points is zero.
Image noiseImage noise is random variation of brightness or color information in s, and is usually an aspect of electronic noise. It can be produced by the and circuitry of a or digital camera. Image noise can also originate in film grain and in the unavoidable shot noise of an ideal photon detector. Image noise is an undesirable by-product of image capture that obscures the desired information. Typically the term “image noise” is used to refer to noise in 2D images, not 3D images.
Complete topological vector spaceIn functional analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get progressively closer to each other, then there exists some point towards which they all get closer. The notion of "points that get progressively closer" is made rigorous by or , which are generalizations of , while "point towards which they all get closer" means that this Cauchy net or filter converges to The notion of completeness for TVSs uses the theory of uniform spaces as a framework to generalize the notion of completeness for metric spaces.
Active noise controlActive noise control (ANC), also known as noise cancellation (NC), or active noise reduction (ANR), is a method for reducing unwanted sound by the addition of a second sound specifically designed to cancel the first. The concept was first developed in the late 1930s; later developmental work that began in the 1950s eventually resulted in commercial airline headsets with the technology becoming available in the late 1980s. The technology is also used in road vehicles, mobile telephones, earbuds, and headphones.
Noise pollutionNoise pollution, or sound pollution, is the propagation of noise or sound with ranging impacts on the activity of human or animal life, most of which are harmful to a degree. The source of outdoor noise worldwide is mainly caused by machines, transport and propagation systems. Poor urban planning may give rise to noise disintegration or pollution, side-by-side industrial and residential buildings can result in noise pollution in the residential areas.
Aircraft noise pollutionAircraft noise pollution refers to noise produced by aircraft in flight that has been associated with several negative stress-mediated health effects, from sleep disorders to cardiovascular ones. Governments have enacted extensive controls that apply to aircraft designers, manufacturers, and operators, resulting in improved procedures and cuts in pollution. Sound production is divided into three categories: Mechanical noise—rotation of the engine parts, most noticeable when fan blades reach supersonic speeds.
