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Deconvolution
In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the signal-to-noise ratio (SNR), the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem. The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'' (1949). The book was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiener Deconvolution
In mathematics, Wiener deconvolution is an application of the Wiener filter to the noise problems inherent in deconvolution. It works in the frequency domain, attempting to minimize the impact of deconvolved noise at frequencies which have a poor signal-to-noise ratio. The Wiener deconvolution method has widespread use in image deconvolution applications, as the frequency spectrum of most visual images is fairly well behaved and may be estimated easily. Wiener deconvolution is named after Norbert Wiener. Definition Given a system: :\ y(t) = (h*x)(t) + n(t) where * denotes convolution and: *\ x(t) is some original signal (unknown) at time \ t . *\ h(t) is the known impulse response of a linear time-invariant system *\ n(t) is some unknown additive noise, independent of \ x(t) *\ y(t) is our observed signal Our goal is to find some \ g(t) so that we can estimate \ x(t) as follows: :\ \hat(t) = (g*y)(t) where \ \hat(t) is an estimate of \ x(t) that minimizes the mean squa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reflection Seismology
Reflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflection (physics), reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite or Tovex blast, a specialized Seismic source#Air gun, air gun or a seismic vibrator. Reflection seismology is similar to sonar and acoustic location, echolocation. History Reflections and refractions of seismic waves at geologic Interface (matter), interfaces within the Earth were first observed on recordings of earthquake-generated seismic waves. The basic model of the Earth's deep interior is based on observations of earthquake-generated seismic waves transmitted through the Earth's interior (e.g., Mohorovičić, 1910). The use of human-generated seismic waves to map in detail the geology of the upper few kilometers of the Earth's crust followed shortly thereafter and has deve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions f and g that produces a third function f*g, as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The term ''convolution'' refers to both the resulting function and to the process of computing it. The integral is evaluated for all values of shift, producing the convolution function. The choice of which function is reflected and shifted before the integral does not change the integral result (see #Properties, commutativity). Graphically, it expresses how the 'shape' of one function is modified by the other. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution f*g differs from cross-correlation f \star g only in that either f(x) or g(x) is reflected about the y-axis in convolution; thus i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seismic
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes (or generally, quakes) and the generation and propagation of elastic waves through planetary bodies. It also includes studies of the environmental effects of earthquakes such as tsunamis; other seismic sources such as volcanoes, plate tectonics, glaciers, rivers, oceanic microseisms, and the atmosphere; and artificial processes such as explosions. Paleoseismology is a related field that uses geology to infer information regarding past earthquakes. A recording of Earth's motion as a function of time, created by a seismograph is called a seismogram. A seismologist is a scientist who works in basic or applied seismology. History Scholarly interest in earthquakes can be traced back to antiquity. Early speculations on the natural causes of earthquakes were included in the writings of Thales of Miletus () ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seismogram
A seismogram is a graph output by a seismograph. It is a record of the ground motion at a measuring station as a function of time. Seismograms typically record motions in three cartesian axes (x, y, and z), with the z axis perpendicular to the Earth's surface and the x- and y- axes parallel to the surface. The energy measured in a seismogram may result from an earthquake or from some other source, such as an explosion. Seismograms can record many things, and record many little waves, called microseisms. These tiny events can be caused by heavy traffic near the seismograph, waves hitting a beach, the wind, and any number of other ordinary things that cause some shaking of the seismograph. Historically, seismograms were recorded on paper attached to rotating drums, a kind of chart recorder. Some used pens on ordinary paper, while others used light beams to expose photosensitive paper. Today, practically all seismograms are recorded digitally to make analysis by computer easier. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Samuelson
Paul Anthony Samuelson (May 15, 1915 – December 13, 2009) was an American economist who was the first American to win the Nobel Memorial Prize in Economic Sciences. When awarding the prize in 1970, the Swedish Royal Academies stated that he "has done more than any other contemporary economist to raise the level of scientific analysis in economic theory". "In a career that spanned seven decades, he transformed his field, influenced millions of students and turned MIT into an economics powerhouse" Samuelson was one of the most influential economists of the latter half of the 20th century."Paul Samuelson: The last of the great general economists died on December 13th, aged 94" ''The Economist'', December 17, 2009 In 1996, he was awarded the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norman Levinson
Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society and in 1971 the Chauvenet Prize (after winning in 1970 the Lester R. Ford Award) of the Mathematical Association of America for his paper ''A Motivated Account of an Elementary Proof of the Prime Number Theorem''. In 1974 he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey. He received both his bachelor's degree and his master's degree in electrical engineering ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enders Robinson
Enders or Ender's may refer to: Literature and film * ''Ender's Game'' (series), a series of science fiction books by Orson Scott Card, also known as the Ender saga ** ''Ender's Game'', a 1985 military science fiction novel ** ''Ender's Shadow'', a 1999 parallel science fiction novel ** '' A War of Gifts: An Ender Story'', a 2007 science fiction novel ** '' Ender in Exile'', a 2008 science fiction novel * ''Ender's Game'' (film), a 2013 American science fiction action film based on the novel Places * Enders, Nebraska, US * Enders, Pennsylvania, US * Enders Island, Connecticut, US People * Arthur Enders (born 1982), also known as "Ace" Enders, former lead singer and guitarist of the defunct band The Early November * Courtney Enders (born 1986), drag racer * Dieter Enders (born 1946), organic chemist who has made contributions to the field of asymmetric synthesis * Erica Enders (born 1983), champion drag racer * John Franklin Enders (1897–1985), Nobel laureate who helpe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
White Noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used with this or similar meanings in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting. White noise refers to a statistical model for signals and signal sources, not to any specific signal. White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band. In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. In some contexts, it is also required that the samples be independent and have identical probability distribution (in other words independent and identically distribu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Filter
Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as sound, images, and scientific measurements. For example, with a filter ''g'', an inverse filter ''h'' is one such that the sequence of applying ''g'' then ''h'' to a signal results in the original signal. Software or electronic inverse filters are often used to compensate for the effect of unwanted environmental filtering of signals. In speech science In all proposed models for the production of human speech, an important variable is the waveform of the airflow, or volume velocity, at the glottis. The glottal volume velocity waveform provides the link between movements of the vocal folds and the acoustical results of such movements, in that the glottis acts approximately as a source of volume velocity. That is, the impedance of the glottis is usually much higher than that of the vocal tract, and so glottal airflow is controlled mostly (but not entirely) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
