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Deconvolution
In mathematics, deconvolution is the operation inverse to 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 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 the fields of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deconvolution Of An Astronomical Image
In mathematics, deconvolution is the operation inverse to 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 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 the fields of ... [...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 reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite or Tovex blast, a specialized air gun or a seismic vibrator. Reflection seismology is similar to sonar and echolocation. This article is about surface seismic surveys; for vertical seismic profiles, see VSP. History Reflections and refractions of seismic waves at geologic 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 h ... [...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 square ... [...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 ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see #Properties, commutativity). The integral is evaluated for all values of shift, producing the convolution function. 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 or is reflected about the y-axis in convolution; thus it is a cross-c ... [...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) by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Source
A point source is a single identifiable ''localised'' source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can usually be approximated as a mathematical point to simplify analysis. The actual source need not be physically small, if its size is negligible relative to other length scales in the problem. For example, in astronomy, stars are routinely treated as point sources, even though they are in actuality much larger than the Earth. In three dimensions, the density of something leaving a point source decreases in proportion to the inverse square of the distance from the source, if the distribution is isotropic, and there is no absorption or other loss. Mathematics In mathematics, a point source is a singularity from which flux or flow is emanating. Although singularities such as this do not exist in the observable universe, mathematical po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the Middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications. As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including but not limited to au ... [...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 and the propagation of elastic waves through the Earth or through other planet-like bodies. It also includes studies of earthquake environmental effects such as tsunamis as well as diverse seismic sources such as volcanic, tectonic, glacial, fluvial, oceanic, atmospheric, and artificial processes such as explosions. A related field that uses geology to infer information regarding past earthquakes is paleoseismology. A recording of Earth motion as a function of time is called a seismogram. A seismologist is a scientist who does research in 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 (c. 585 BCE), Anaximenes of Miletus (c. 550 BCE), Aristotle (c. 340 BCE), and Zhan ... [...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 microseisms 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 eas ... [...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" Economic historian Randall E. Parker has called him the "Father of Modern Economics", and ''The New York Times'' considers him to be the "foremost academic economist of the 20th century". Samuelson was likely the most influential economist of the latter half of the 20th century."Paul ... [...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 from ... [...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 helped develo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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