The median is the value separating the higher half from the lower half of a data sample. For a data set, it may be thought of as the "middle" value. For example, in the data set, the median is 6, the fourth largest, the fifth smallest, number in the sample. For a continuous probability distribution, the median is the value such that a number is likely to fall above or below it; the median is a used measure of the properties of a data set in statistics and probability theory. The basic advantage of the median in describing data compared to the mean is that it is not skewed so much by large or small values, so it may give a better idea of a "typical" value. For example, in understanding statistics like household income or assets which vary a mean may be skewed by a small number of high or low values. Median income, for example, may be a better way to suggest; because of this, the median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median will not give an arbitrarily large or small result.
The median of a finite list of numbers can be found by arranging all the numbers from smallest to greatest. If there is an odd number of numbers, the middle one is picked. For example, consider the list of numbers 1, 3, 3, 6, 7, 8, 9This list contains seven numbers; the median is the fourth of them, 6. If there is an number of observations there is no single middle value. For example, in the data set 1, 2, 3, 4, 5, 6, 8, 9the median is the mean of the middle two numbers: this is / 2, 4.5.. The formula used to find the index of the middle number of a data set of n numerically ordered numbers is / 2; this either gives the halfway point between the two middle values. For example, with 14 values, the formula will give an index of 7.5, the median will be taken by averaging the seventh and eighth values. So the median can be represented by the following formula: m e d i a n = a ⌈ # x ÷ 2 ⌉ + a ⌈ # x ÷ 2 + 1 ⌉ 2 One can find the median using the Stem-and-Leaf Plot. There is no accepted standard notation for the median, but some authors represent the median of a variable x either as x͂ or as μ1/2 sometimes M.
In any of these cases, the use of these or other symbols for the median needs to be explicitly defined when they are introduced. The median is used for skewed distributions, which it summarizes differently from the arithmetic mean. Consider the multiset; the median is 2 in this case, it might be seen as a better indication of central tendency than the arithmetic mean of 4. The median is a popular summary statistic used in descriptive statistics, since it is simple to understand and easy to calculate, while giving a measure, more robust in the presence of outlier values than is the mean; the cited empirical relationship between the relative locations of the mean and the median for skewed distributions is, not true. There are, various relationships for the absolute difference between them. With an number of observations no value need be at the value of the median. Nonetheless, the value of the median is uniquely determined with the usual definition. A related concept, in which the outcome is forced to correspond to a member of the sample, is the medoid.
In a population, at most half have values less than the median and at most half have values greater than it. If each group contains less than half the population some of the population is equal to the median. For example, if a < b < c the median of the list is b, and, if a < b < c < d the median of the list is the mean of b and c. Indeed, as it is based on the middle data in a group, it is not necessary to know the value of extreme results in order to calculate a median. For example, in a psychology test investigating the time needed to solve a problem, if a small number of people failed to solve the problem at all in the given time a median can still be calculated; the median can be used as a measure of location when a distribution is skewed, when end-values are not known, or when one requires reduced importance to be attached to outliers, e.g. because they may be measurement errors. A median is only defined on ordered one-dimensional data, is independent of any distance metric. A geometric median, on the other hand, is defined in any number of dimensions.
The median is one of a number of ways
Signal processing is a subfield of mathematics and electrical engineering that concerns the analysis and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound and biological measurements. For example, signal processing techniques are used to improve signal transmission fidelity, storage efficiency, subjective quality, to emphasize or detect components of interest in a measured signal. According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. Oppenheim and Schafer further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. Analog signal processing is for signals that have not been digitized, as in legacy radio, telephone and television systems; this involves linear electronic circuits as well as non-linear ones. The former are, for instance, passive filters, active filters, additive mixers and delay lines.
Non-linear circuits include compandors, voltage-controlled filters, voltage-controlled oscillators and phase-locked loops. Continuous-time signal processing is for signals; the methods of signal processing include time domain, frequency domain, complex frequency domain. This technology discusses the modeling of linear time-invariant continuous system, integral of the system's zero-state response, setting up system function and the continuous time filtering of deterministic signals Discrete-time signal processing is for sampled signals, defined only at discrete points in time, as such are quantized in time, but not in magnitude. Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers, analog delay lines and analog feedback shift registers; this technology was a predecessor of digital signal processing, is still used in advanced processing of gigahertz signals. The concept of discrete-time signal processing refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.
Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors. Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued and addition. Other typical operations supported by the hardware are circular buffers and lookup tables. Examples of algorithms are the Fast Fourier transform, finite impulse response filter, Infinite impulse response filter, adaptive filters such as the Wiener and Kalman filters. Nonlinear signal processing involves the analysis and processing of signals produced from nonlinear systems and can be in the time, frequency, or spatio-temporal domains. Nonlinear systems can produce complex behaviors including bifurcations, chaos and subharmonics which cannot be produced or analyzed using linear methods. Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks.
Statistical techniques are used in signal processing applications. For example, one can model the probability distribution of noise incurred when photographing an image, construct techniques based on this model to reduce the noise in the resulting image. Audio signal processing – for electrical signals representing sound, such as speech or music Speech signal processing – for processing and interpreting spoken words Image processing – in digital cameras and various imaging systems Video processing – for interpreting moving pictures Wireless communication – waveform generations, filtering, equalization Control systems Array processing – for processing signals from arrays of sensors Process control – a variety of signals are used, including the industry standard 4-20 mA current loop Seismology Financial signal processing – analyzing financial data using signal processing techniques for prediction purposes. Feature extraction, such as image understanding and speech recognition. Quality improvement, such as noise reduction, image enhancement, echo cancellation.
Including audio compression, image compression, video compression. Genomics, Genomic signal processing In communication systems, signal processing may occur at: OSI layer 1 in the seven layer OSI model, the Physical Layer. Filters – for example analog or digital Samplers and analog-to-digital converters for signal acquisition and reconstruction, which involves measuring a physical signal, storing or transferring it as digital signal, later rebuilding the original signal or an approximation thereof. Signal compressors Digital signal processors Differential equations Recurrence relation Transform theory Time-frequency analysis – for processing non-stationary signals Spectral estimation – for determining the spectral content of a
ArXiv is a repository of electronic preprints approved for posting after moderation, but not full peer review. It consists of scientific papers in the fields of mathematics, astronomy, electrical engineering, computer science, quantitative biology, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics all scientific papers are self-archived on the arXiv repository. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, had hit a million by the end of 2014. By October 2016 the submission rate had grown to more than 10,000 per month. ArXiv was made possible by the compact TeX file format, which allowed scientific papers to be transmitted over the Internet and rendered client-side. Around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Paul Ginsparg recognized the need for central storage, in August 1991 he created a central repository mailbox stored at the Los Alamos National Laboratory which could be accessed from any computer.
Additional modes of access were soon added: FTP in 1991, Gopher in 1992, the World Wide Web in 1993. The term e-print was adopted to describe the articles, it began as a physics archive, called the LANL preprint archive, but soon expanded to include astronomy, computer science, quantitative biology and, most statistics. Its original domain name was xxx.lanl.gov. Due to LANL's lack of interest in the expanding technology, in 2001 Ginsparg changed institutions to Cornell University and changed the name of the repository to arXiv.org. It is now hosted principally with eight mirrors around the world, its existence was one of the precipitating factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists upload their papers to arXiv.org for worldwide access and sometimes for reviews before they are published in peer-reviewed journals. Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv; the annual budget for arXiv is $826,000 for 2013 to 2017, funded jointly by Cornell University Library, the Simons Foundation and annual fee income from member institutions.
This model arose in 2010, when Cornell sought to broaden the financial funding of the project by asking institutions to make annual voluntary contributions based on the amount of download usage by each institution. Each member institution pledges a five-year funding commitment to support arXiv. Based on institutional usage ranking, the annual fees are set in four tiers from $1,000 to $4,400. Cornell's goal is to raise at least $504,000 per year through membership fees generated by 220 institutions. In September 2011, Cornell University Library took overall administrative and financial responsibility for arXiv's operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it "was supposed to be a three-hour tour, not a life sentence". However, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. Although arXiv is not peer reviewed, a collection of moderators for each area review the submissions; the lists of moderators for many sections of arXiv are publicly available, but moderators for most of the physics sections remain unlisted.
Additionally, an "endorsement" system was introduced in 2004 as part of an effort to ensure content is relevant and of interest to current research in the specified disciplines. Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, but to check whether the paper is appropriate for the intended subject area. New authors from recognized academic institutions receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for restricting scientific inquiry. A majority of the e-prints are submitted to journals for publication, but some work, including some influential papers, remain purely as e-prints and are never published in a peer-reviewed journal. A well-known example of the latter is an outline of a proof of Thurston's geometrization conjecture, including the Poincaré conjecture as a particular case, uploaded by Grigori Perelman in November 2002.
Perelman appears content to forgo the traditional peer-reviewed journal process, stating: "If anybody is interested in my way of solving the problem, it's all there – let them go and read about it". Despite this non-traditional method of publication, other mathematicians recognized this work by offering the Fields Medal and Clay Mathematics Millennium Prizes to Perelman, both of which he refused. Papers can be submitted in any of several formats, including LaTeX, PDF printed from a word processor other than TeX or LaTeX; the submission is rejected by the arXiv software if generating the final PDF file fails, if any image file is too large, or if the total size of the submission is too large. ArXiv now allows one to store and modify an incomplete submission, only finalize the submission when ready; the time stamp on the article is set. The standard access route is through one of several mirrors. Sev
Burst noise is a type of electronic noise that occurs in semiconductors and ultra-thin gate oxide films. It is called random telegraph noise, popcorn noise, impulse noise, bi-stable noise, or random telegraph signal noise, it consists of sudden step-like transitions between two or more discrete voltage or current levels, as high as several hundred microvolts, at random and unpredictable times. Each shift in offset voltage or current lasts from several milliseconds to seconds, sounds like popcorn popping if hooked up to an audio speaker. Popcorn noise was first observed in early point contact diodes re-discovered during the commercialization of one of the first semiconductor op-amps. No single source of popcorn noise is theorized to explain all occurrences, however the most invoked cause is the random trapping and release of charge carriers at thin film interfaces or at defect sites in bulk semiconductor crystal. In cases where these charges have a significant impact on transistor performance, the output signal can be substantial.
These defects can be caused by manufacturing processes, such as heavy ion implantation, or by unintentional side-effects such as surface contamination. Individual op-amps can be screened for popcorn noise with peak detector circuits, to minimize the amount of noise in a specific application. Burst noise is modeled mathematically by means of the telegraph process, a Markovian continuous-time stochastic process that jumps discontinuously between two distinct values. Atomic electron transition Telegraph process A review of popcorn noise and smart filtering, www.advsolned.com
Noise pollution known as environmental noise or sound pollution, is the propagation of noise with harmful impact on the activity of human or animal life. The source of outdoor noise worldwide is caused by machines and propagation systems. Poor urban planning may give rise to noise pollution, side-by-side industrial and residential buildings can result in noise pollution in the residential areas; some of the main sources of noise in residential areas include loud music, transportation noise, lawn care maintenance, nearby construction, or young people yelling. Noise pollution associated with household electricity generators is an emerging environmental degradation in many developing nations; the average noise level of 97.60 dB obtained exceeded the WHO value of 50 dB allowed for residential areas. Research suggests that noise pollution is the highest in low-income and racial minority neighborhoods. Documented problems associated with urban environment noise go back as far as ancient Rome. High noise levels can contribute to cardiovascular effects in humans and an increased incidence of coronary artery disease.
In animals, noise can increase the risk of death by altering predator or prey detection and avoidance, interfere with reproduction and navigation, contribute to permanent hearing loss. While the elderly may have cardiac problems due to noise, according to the World Health Organization, children are vulnerable to noise, the effects that noise has on children may be permanent. Noise poses a serious threat to a child’s physical and psychological health, may negatively interfere with a child's learning and behavior. Noise pollution affects both behavior. Unwanted sound can damage physiological health. Noise pollution can cause hypertension, high stress levels, hearing loss, sleep disturbances, other harmful effects. Sound becomes unwanted when it either interferes with normal activities such as sleep or conversation, or disrupts or diminishes one's quality of life. Noise-induced hearing loss can be caused by prolonged exposure to noise levels above 85 A-weighted, decibels. A comparison of Maaban tribesmen, who were insignificantly exposed to transportation or industrial noise, to a typical U.
S. population showed that chronic exposure to moderately high levels of environmental noise contributes to hearing loss. Noise exposure in the workplace can contribute to noise-induced hearing loss and other health issues. Occupational hearing loss is one of the most common work-related illnesses in the U. S. and worldwide. Less addressed is. Indeed, tolerance for noise is independent of decibel levels. However, Murray Schafer's soundscape research was groundbreaking in this regard. In his eponymous work, he makes compelling arguments about how humans relate to noise on a subjective level, how such subjectivity is conditioned by culture, he notes that sound is an expression of power, as such, material culture tend to have louder engines not only for safety reasons, but for expressions of power by dominating the soundscape with a particular sound. Other key research in this area can be seen in Fong's comparative analysis of soundscape differences between Bangkok and Los Angeles, California, US. Based on Schafer's research, Fong's study showed how soundscapes differ based on the level of urban development in the area.
He found. Fong's important findings tie not only soundscape appreciation to our subjective views of sound, but demonstrates how different sounds of the soundscape are indicative of class differences in urban environments. Noise pollution can have negative affects on children on the autistic spectrum; those with Autism Spectrum Disorder can have hyperacusis, an abnormal sensitivity to sound. People with ASD that experience hyperacusis may have unpleasant emotions, such as fear and anxiety, sensations in noisy environments with loud sounds; this can cause individuals with ASD to avoid environments with noise pollution which can cause isolation and negatively impact their quality of life. Sudden explosive noises typical of high-performance car exhausts and car alarms are types of noise pollution that can affect individuals with ASD. Noise can have a detrimental effect on animals, increasing the risk of death by changing the delicate balance in predator or prey detection and avoidance, interfering the use of the sounds in communication in relation to reproduction and in navigation.
These effects may alter more interactions within a community through indirect effects. Acoustic overexposure can lead to permanent loss of hearing. European robins living in urban environments are more to sing at night in places with high levels of noise pollution during the day, suggesting that they sing at night because it is quieter, their message can propagate through the environment more clearly; the same study showed that daytime noise was a stronger predictor of nocturnal singing than night-time light pollution, to which the phenomenon is attributed. Anthropogenic noise reduced the species richness of birds found in Neoptropical urban parks. Zebra finches become less faithful to their partners; this could alter a population's evolutionary trajectory by selecting traits, sapping resources devoted to other activities and thus leading to profound genetic and evolutionary consequences. Underwater noise pollution due to human activities is prevalent in the sea. Cargo ships generate high levels of noise due to diesel engines.
This noise pollutio
Edge detection includes a variety of mathematical methods that aim at identifying points in a digital image at which the image brightness changes or, more formally, has discontinuities. The points at which image brightness changes are organized into a set of curved line segments termed edges; the same problem of finding discontinuities in one-dimensional signals is known as step detection and the problem of finding signal discontinuities over time is known as change detection. Edge detection is a fundamental tool in image processing, machine vision and computer vision in the areas of feature detection and feature extraction; the purpose of detecting sharp changes in image brightness is to capture important events and changes in properties of the world. It can be shown that under rather general assumptions for an image formation model, discontinuities in image brightness are to correspond to: discontinuities in depth, discontinuities in surface orientation, changes in material properties and variations in scene illumination.
In the ideal case, the result of applying an edge detector to an image may lead to a set of connected curves that indicate the boundaries of objects, the boundaries of surface markings as well as curves that correspond to discontinuities in surface orientation. Thus, applying an edge detection algorithm to an image may reduce the amount of data to be processed and may therefore filter out information that may be regarded as less relevant, while preserving the important structural properties of an image. If the edge detection step is successful, the subsequent task of interpreting the information contents in the original image may therefore be simplified. However, it is not always possible to obtain such ideal edges from real life images of moderate complexity. Edges extracted from non-trivial images are hampered by fragmentation, meaning that the edge curves are not connected, missing edge segments as well as false edges not corresponding to interesting phenomena in the image – thus complicating the subsequent task of interpreting the image data.
Edge detection is one of the fundamental steps in image processing, image analysis, image pattern recognition, computer vision techniques. The edges extracted from a two-dimensional image of a three-dimensional scene can be classified as either viewpoint dependent or viewpoint independent. A viewpoint independent edge reflects inherent properties of the three-dimensional objects, such as surface markings and surface shape. A viewpoint dependent edge may change as the viewpoint changes, reflects the geometry of the scene, such as objects occluding one another. A typical edge might for instance be the border between a block of yellow. In contrast a line can be a small number of pixels of a different color on an otherwise unchanging background. For a line, there may therefore be one edge on each side of the line. Although certain literature has considered the detection of ideal step edges, the edges obtained from natural images are not at all ideal step edges. Instead they are affected by one or several of the following effects: focal blur caused by a finite depth-of-field and finite point spread function.
Penumbral blur caused by shadows created by light sources of non-zero radius. Shading at a smooth objectA number of researchers have used a Gaussian smoothed step edge as the simplest extension of the ideal step edge model for modeling the effects of edge blur in practical applications. Thus, a one-dimensional image f which has one edge placed at x = 0 may be modeled as: f = I r − I l 2 + I l. At the left side of the edge, the intensity is I l = lim x → − ∞ f, right of the edge it is I r = lim x → ∞ f; the scale parameter σ is called the blur scale of the edge. Ideally this scale parameter should be adjusted based on the quality of image to avoid destroying true edges of the image. To illustrate why edge detection is not a trivial task, consider the problem of detecting edges in the following one-dimensional signal. Here, we may intuitively say that there should be an edge between the 5th pixels. If the intensity difference were smaller between the 4th and the 5th pixels and if the intensity differences between the adjacent neighboring pixels were higher, it would not be as easy to say that there should be an edge in the corresponding region.
Moreover, one could argue. Hence, to state a specific threshold on how large the intensity change between two neighbouring pixels must be for us to say that there should be an edge between these pixels is not always simple. Indeed, this is one of the reasons why edge detection may be a non-trivial problem unless the objec
Noise 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, occupational noise control. Roadway noise and aircraft noise are the most pervasive sources of environmental noise. Social activities may generate noise levels that affect the health of populations residing in or occupying areas, both indoor and outdoor, near entertainment venues that feature amplified sounds and music that present significant challenges for effective noise mitigation strategies. Multiple techniques have been developed to address interior sound levels, many of which are encouraged by local building codes. In the best case of project designs, planners are encouraged to work with design engineers to examine trade-offs of roadway design and architectural design; these techniques include design of exterior walls, party walls, floor and ceiling assemblies.
Many of these techniques rely upon material science applications of constructing sound baffles or using sound-absorbing liners for interior spaces. Industrial noise control is a subset of interior architectural control of noise, with emphasis on specific methods of sound isolation from industrial machinery and for protection of workers at their task stations. Sound masking is the active addition of noise to reduce the annoyance of certain sounds. Organizations each have their own standards, recommendations/guidelines, directives for what levels of noise workers are permitted to be around before noise controls must be put into place. OSHA's requirements state that when workers are exposed to noise levels above 90 A-weighted decibels in 8-hour time-weighted averages, administrative controls and/or new engineering controls must be implemented in the workplace. OSHA requires that impulse noises and impact noises must be controlled to prevent these noises reaching past 140 dB peak sound pressure levels.
MSHA requires that administrative and/or engineering controls must be implemented in the workplace when miners are exposed to levels above 90 dBA TWA. If noise levels exceed 115 dBA, miners are required to wear hearing protection. MSHA, requires that noise levels be reduced below 115 dB TWA. Measuring noise levels for noise control decision making must integrate all noises from 90dBA to 140 dBA; the FRA recommends that worker exposure to noise should be reduced when their noise exposure exceeds 90 dBA for an 8-hour TWA. Noise measurements must integrate all noises, including intermittent, continuous and impulse noises between 80 dBA to 140 dBA; the DoD suggests that noise levels be controlled through engineering controls. The DoD requires that all steady-state noises be reduced to levels below 85 dBA and that impulse noises be reduced below 140 dB peak SPL. Time Weighted Average exposures are not considered for the DoD's requirements; the European Parliament and Council directive require noise levels to be reduced or eliminated using administrative and engineering controls.
This directive requires lower exposure action levels of 80 dBA for 8 hours with 135 dB peak SPL, along with upper exposure action levels of 85 dBA for 8 hours with 137 peak dBSPL. Exposure limits are 87 dBA for 8 hours with peak levels of 140 peak dBSPL. An effective model for noise control is the source and receiver model by Bolt and Ingard. Hazardous noise can be controlled by reducing the noise output at its source, minimizing the noise as it travels along a path to the listener, providing equipment to the listener or receiver to attenuate the noise. A variety of measures aim to reduce hazardous noise at its source. Programs such as Buy Quiet and the National Institute for Occupational Safety and Health Prevention through design promote research and design of quiet equipment and renovation and replacement of older hazardous equipment with modern technologies. Physical materials, such as foam, absorb sound and walls to provide a sound barrier that modifies existing systems that decrease hazardous noise at the source.
The principle of noise reduction through pathway modifications applies to the alteration of direct and indirect pathways for noise. Noise that travels across reflective surfaces, such as smooth floors, can be hazardous. Pathway alterations include sound dampening enclosures for loud equipment and isolation chambers from which workers can remotely control equipment while removed from noise; these methods prevent sound from traveling along a path to other listener. In the industrial or commercial setting, workers must comply with the appropriate Hearing conservation program. Administrative controls, such as the restriction of personnel in noisy areas, prevents unnecessary noise exposure. Personal protective equipment such as foam ear plugs or ear muffs to attenuate sound provide a last line of defense for the listener. Sound insulation: prevent the transmission of noise by the introduction of a mass barrier. Common materials have high-density properties such as brick, thick glass, metal etc. Sound absorption: a porous material which acts as a ‘noise sponge’ by converting the sound energy into heat within the material.
Common sound absorption materials include decoupled lead-based tiles, open cell foams and fiberglass Vibration damping: applicable for large vibrating surfaces. The damping mechanism works by extracting the vibration energy from the thin sheet and dissipating it as heat. A co