No footnotes date September 2008 Image Spectral lines continous.png thumb Continuous spectrum Image Spectral lines emission.png thumb Emission spectrum Emission lines Image Spectral lines absorption.png thumb Absorption spectroscopy Absorption lines A spectralline is a dark or bright line in an otherwise ... in a narrow frequency range, compared with the nearby frequencies. Types of line spectra Spectral lines are the result of interaction between a quantum system usually atomic spectralline atoms ... line . If the detector sees the gas, but not the original photon source, then the detector will see the photons reemitted in a narrow frequency range. This will be an emission line . Spectral ... spectral series series , such as the Lyman series or Balmer series . Spectralline broadening and shift A spectralline extends over a range of frequencies, not a single frequency i.e., it has .... Since the spectralline is a combination of all of the emitted radiation, the higher the temperature of the gas, the broader will be the spectralline emitted from that gas. This broadening effect ... narrowing , known as the Dicke effect . See also Absorption spectrum Atomic spectralline ... isbn 0 521 45504 9 cite book first Hans R. last Griem year 1974 title SpectralLine Broadening by Plasmas ... SpectralLine Category Spectroscopy Category Emission spectroscopy bg ca L nia ... Spectralline sk Spektr lna iara fi Spektriviiva sv Spektrallinje th tr Tayf izgileri ... line or an absorption line will be produced. If the gas is between the photon source and the detector ... by spectroscopic means, such as helium , thallium , and cerium . Spectral lines also depend on the physical ... conditions. Isomer shift is the displacement of an absorption line due to the absorbing nuclei having ... interaction can produce spectral lines. Depending on the exact physical interaction with molecules ... date October 2008 Strong spectral lines in the visible spectrum visible part of the spectrum ... more details
Linespectral pairs LSP or linespectral frequencies LSF are used to represent linear predictive coding linear prediction coefficients LPC for transmission over a channel. LSPs have several properties e.g. smaller sensitivity to quantization noise that make them superior to direct quantization of LPCs. For this reason, LSPs are very useful in speech coding . Mathematical foundation The LP polynomial math A z 1 sum k 1 p a k z k math can be decomposed into math P z A z z p 1 A z 1 math math Q z A z z p 1 A z 1 math where P z corresponds to the vocal tract with the glottis closed and Q z with the glottis open. While A z has complex roots anywhere within the unit circle z transform , P z and Q z have the very useful property of only having roots on the unit circle, hence P is a palindromic polynomial and Q an antipalindromic polynomial . So to find them we take a test point math z exp jw math and evaluate math P exp jw math and math Q exp jw math using a grid of points between 0 and pi. The zeros roots of P z and Q z also happen to be interspersed which is why we swap coefficients as we find roots. So the process of finding the LSP frequencies is basically finding the roots of two polynomials of order p 1. The roots of P z and Q z occur in symmetrical pairs at w , hence the name Line Spectrum Pairs LSPs . Because all the roots are complex and two roots are found at 0 and math pi math , only p 2 roots need to be found for each polynomial. The output of the LSP search thus ... used for quantizing LPC filters. Linespectral frequencies can be interpolated. See also Log ... www.ece.mcgill.ca pkabal papers 1986 Kabal1986.pdf The Computation of LineSpectral Frequencies Using ... pdf lsp.pdf LineSpectral Pairs chapter as an online excerpt pdf Digital Signal Processing ... through it N times order of the filter , yielding the original filter, A z . Properties Linespectral pairs have several interesting and useful properties. When the roots of P z and Q z are interleaved ... more details
or absorbed in the process. The frequency math nu math at which the spectralline occurs is related ... is more complicated. The above equations have ignored the influence of the spectralline shape. To be accurate, the above equations need to be multiplied by the normalized spectralline ... three processes occurring in the formation of an atomic spectralline. The three processes are referred ... in terms of the single oscillator strength associated with the particular atomic spectralline math ...No footnotes date September 2008 Image Spectral lines en.PNG thumb Emission lines and absorption lines compared to a continuous spectrum. In physics , atomic spectral lines are of two types An emission line is formed when an electron makes a transition from a particular discrete energy level of an atom, to a lower energy state, emitting a photon of a particular energy and wavelength. A spectrum of many such photons will show an emission spike at the wavelength associated with these photons. An absorption line is formed when an electron makes a transition from a lower to a higher discrete energy state, with a photon being absorbed in the process. These absorbed photons generally come from background ... s constant . Emission and absorption coefficients The emission of atomic line radiation may be described ... math d Omega math . For atomic line radiation math epsilon frac h nu 4 pi n 2 A 21 , math where ... kappa frac h nu 4 pi n 1 B 12 n 2 B 21 , math where math I nu math is the spectral intensity of radiation ... actually produces photons within a narrow range of frequencies called the spectral linewidth ... the probability per unit time per unit spectral radiance of the radiation field that an electron ... s sup &minus 1 sup , which gives the probability per unit time per unit spectral radiance of the radiation ... . From Planck s law of black body radiation we have for the spectral radiance at frequency math ... energy density is used rather than the spectral radiance, in which case math F nu frac 8 pi ... more details
Summary Information Description Spectralline radiation from a xenon flashtube operated at high voltage and low current. The tube was under energized to allow the camera to photograph it unfiltered. Although the greenish blue arc looks similar to the flash appearance to the naked eye, the bright blue reflected off the table was not visible. This is caused by the camera being able to image the strong infrared lines around 900 nm, ref https kb.osu.edu dspace bitstream 1811 5654 1 V71N06 343.pdf ref which the camera sees as blue. ref http www.beyondvisible.com BV3 FS3P.html ref Source I User Zaereth Zaereth User talk Zaereth talk created this work entirely by myself. Date 18 28, 14 September 2009 UTC Author User Zaereth Zaereth User talk Zaereth talk other versions References references Licensing PD self date September 2009 ... more details
Summary Information Description This photo shows the spectralline radiation from a krypton arc lamp. While the light looked almost white to the human eye, the camera images the very strong infrared line at 820 nanometers as purple. Source I User Zaereth Zaereth User talk Zaereth talk created this work entirely by myself. Date 20 10, 22 January 2010 UTC Author User Zaereth Zaereth User talk Zaereth talk other versions Licensing PD self date January 2010 ... more details
Unreferenced stub auto yes date December 2009 Mergeto Full Spectral Imaging date July 2010 Spectral imaging is a branch of spectroscopy in which a complete spectrum or some spectral information such as the Doppler shift or Zeeman splitting of a spectralline is collected at every location in an image plane . Applications include astronomy , solar physics , analysis of Plasma physics plasmas in nuclear fusion experiments, planetology , and Earth remote sensing . This is often referred to as hyperspectral imaging . See also Dopplergraph Imaging spectrometer DEFAULTSORT Spectral Imaging Category Astronomical spectroscopy Physics stub ... more details
Spectral analysis or Spectrum analysis may refer to Spectrum analysis in chemistry and physics, a method of analyzing the chemical properties of matter from bands in their visible spectrum Spectrum analyzer in signal processing, a device or algorithm that identifies a frequency domain representation of a time domain signal, typically by means of Fourier transform Spectral theory , in mathematics, a theory that extends eigenvalues and eigenvectors to linear operators on Hilbert space, and more generally to the elements of a Banach algebra Spectral analysis in statistics, a procedure that decomposes a time series into a spectrum of cycles of different lengths. Spectral analysis is also known as frequency domain analysis In nuclear and particle physics, gamma spectroscopy , and high energy astronomy, the analysis of the output of a pulse height analyzer for characteristic features such as spectralline , edges, and various physical processes producing continuum shapes disambig ... more details
on the line of purples , which are various mixtures of violet and red light. See also Imaginary color DEFAULTSORT Spectral Color Category Color Color stub ar de Spektralfarbe eo Spektrokoloro ... more details
Unreferenced date December 2009 The spectral linewidth characterizes the width of a spectralline , such as in the emission spectrum electromagnetic emission spectrum of an atom, or the frequency spectrum of an acoustic or electronic system. For example, the emission of an atom usually has a very thin spectral linewidth, as only transitions between discrete energy levels are allowed, leading to emission of photons with a certain energy. Several definitions are used to quantify the spectral linewidth, e.g. the full width at half maximum FWHM . While the spectral width of a resonator in electronics depends on the parameters of the components, and therefore can be easily adjusted over a wide range, linewidths are typically more difficult to adjust in physics. For example, even a resting atom which does not interact with its environment has a non zero linewidth , called the natural linewidth also called the decay width , which is a consequence of the Fourier transform Localization property Fourier transform limit classical description and the Heisenberg uncertainty principle quantum mechanical description . According to the uncertainty principle the uncertainty in energy, E , of a transition is inversely proportional to the lifetime, t of the excited state math Delta E Delta t gtrapprox frac hbar 2 . math In practice lines are further broadened by effects such as Doppler broadening . See also Bandwidth signal processing , a more generic term for a range of electromagnetic frequencies Q factor and linewidths in electronics, acoustics and optics Spectralline s in optics. This article also includes a list of sources of linewidth broadening. Spectral width in telecommunications Oscillator linewidth Laser linewidth DEFAULTSORT Spectral Linewidth Category Optics de Linienbreite lb Spektral Linnebreet tr Spektral izgi geni li i uk ... more details
A spectral glide is a modification of the vowel quality of a tone Erickson 1975, p. 72 . Since the vowel quality of a pitch music tone is determined by the overtone s, spectrum , or timbre all three terms being near equal of that tone, a spectral glide is a move from one spectrum characteristic of a vowel to another. A spectral glide may be accomplished through a wah wah music wah wah mute or pedal or through the modification of one s vocal tract while speaking, singing, or playing an instrument such as the didgeridoo . Buzzed lip instruments with large mouthpieces such as tuba and trombone allow extensive modification of vowel quality while woodwinds have a smaller range with the exception of the flute in air sound mode. Strings have the smallest range. ibid Important in the compositional use of spectral glides is the glide rate and the vowel contrasts used. Karlheinz Stockhausen specifies the use of a trumpet mute in his Punkte 1952 1962 through open and closed circles connected by a line. A. Wayne Slawson s computer generated Wishful Thinking about Winter Decca DL 710180 uses speechlike sounds featuring a large range of spectral glide rates. Loren Rush began investigating in 1967 the computer generated modeling of timbres in between familiar instruments such as a bassoon and bass clarinet and devised a program to provide a smooth transition between timbres. ibid, p. 73 Source Erickson, Robert 1975 . Sound Structure in Music . University of California Press. ISBN 0 520 02376 5. DEFAULTSORT Spectral Glide Category Musical performance techniques Category Vowels Category Timbre ... more details
, which produces a single number indicating the slope of the line of best fit through the spectral ...In astrophysics and planetary science , spectral slope , also called spectral gradient , is a measure of dependence of the reflectance on the wavelength . In digital signal processing , it is a measure of how quickly the spectrum of an audio sound tails off towards the high frequencies, calculated using a linear regression ref name Peeters04 G. Peeters, http recherche.ircam.fr equipes analyse synthese peeters ARTICLES Peeters 2003 cuidadoaudiofeatures.pdf A large set of audio features for sound description , tech. rep., IRCAM, 2004. ref . Image TheSpectralSlope.png thumb 300px right Illustration of the spectral slope Spectral slope in Astrophysics Planetary Science The visible and infrared electromagnetic spectrum spectrum of the reflected sunlight is used to infer physical and chemical properties of the surface of a body. Some objects are brighter reflect more in longer wavelengths red . Consequently, in visible light they will appear redder than objects showing no dependence of reflectance on the wavelength. The diagram illustrates three slopes a red slope , the reflectance is increasing with the wavelengths flat spectrum in black And a blue slope , the reflectance actually diminishing with the wavelengths The slope spectral gradient is defined as math S frac R F 1 R F 0 lambda 1 lambda 0 math where math R F 0 , R F 1 math is the reflectance measured with filters F sub 0 sub , F sub 1 sub having the central wavelengths sub 0 sub and sub 1 sub , respectively. ref name ArizonaBook Doressoundiram2007 Cite journal author A. Deressoundiram, H. Boehnhardt, S. Tegler and Chad ... spectrum appears flat in near infra red. Spectral slope in audio The spectral slope of many natural ... vs frequency include spectral rolloff , spectral centroid ref name Peeters04 . See also roll ... stub Signal processing stub fr Gradient spectral ... more details
Unreferenced date April 2007 Spectral bands are part of optical spectra of polyatomic systems, including condensed materials, large molecules etc. Each line corresponding to one level in atom splits in molecules. When the number of atoms is large, one gets continuum of energy levels, so called spectral bands . They are often labeled in the same way as the monoatomic lines. The bands may overlap. In general, energy spectrum can be given with a density function, describing the number of energy levels of the quantum system for a given interval. Spectral bands have constant density, and when the bands overlap, the corresponding densities are added. Band spectra is the name given to group of lines that are closely spaced, arranging in a regular sequence that appears to be a band. It is a coloured band, separated by dark space on the two sides, arranged in regular sequence. In one band, there are various sharp and wider colour lines that are closer on one side, and wider on other side. The intensity in each band falls off from definite limits, and indistinct on the other side. In complete band spectra, there is a number lines in a band. This spectra is produced, when the emitting substance is in the molecular state. Therefore, they are also called molecular spectra. It is emitted by a molecule in vacuum tube , C arc core with metallic salt. Band spectra is the combinations of many different spectrallinespectral lines , resulting from rotational, vibrational and Molecular electronic transition electronic transition . See also Band emission Category Spectroscopy physics stub fr Bande spectrale hr Spektroskopska vrpca ... more details
modulation rate or line code pulse rate. Link spectral efficiency is typically used to analyse the efficiency of a digital modulation method or line code , sometimes in combination with a forward error ...Spectral efficiency , spectrum efficiency or bandwidth efficiency refers to the information rate that can ... protocol, and sometimes by the media access control the channel access protocol . Link spectral efficiency The link spectral efficiency of a digital communication system is measured in bit second ... or a data link . Alternatively, the spectral efficiency may be measured in in bit symbol , which is equivalent ... of 3,400 300 3,100 hertz. The spectral efficiency or modulation efficiency is 56,000 3,100 18.1 ... efficiency measured in bit symbol or bpcu . In the case of baseband transmission line coding ... can not exceed 2 B symbols s in view to avoid intersymbol interference . Thus, the spectral efficiency ... 4 bit symbol or bpcu. Since QAM is a form of double sideband passband transmission, the spectral ... signal before passband filtering can be considered as baseband transmission, the spectral efficiency ..., a higher spectral efficiency is achieved if we consider the smaller passband bandwidth. If a forward error correction code is used, the spectral efficiency is reduced from the uncoded modulation ... that the encoder input bit rate is one half the encoder output rate, the spectral efficiency is 50 of the modulation efficiency. In exchange for this reduction in spectral efficiency, FEC usually ... . An upper bound for the spectral efficiency possible without bit error s in a channel with a certain ... 7 If the SNR is 1 times expressed as a ratio, corresponding to 0 decibel , the link spectral efficiency ... is not already efficiently compressed. The link spectral efficiency of a wireless telephony link ..., the link spectral efficiency can be somewhat misleading, as larger values are not necessarily more efficient in their overall use of radio spectrum. In a wireless network, high link spectral ... more details
unreferenced date February 2008 In telecommunications , a spectral mask , also known as a channel mask or transmission mask, is a math ematically defined set of line mathematics lines applied to the levels of radio or optical transmission telecommunications transmission s. The spectral mask is generally intended to reduce adjacent channel interference by limiting excessive radiation at frequencies beyond the necessary bandwidth signal processing bandwidth . Attenuation of these spurious emission s is usually done with a band pass filter , Tuned filter tuned to allow through the correct center frequency of the carrier wave , as well as all necessary sideband s. The spectral mask is usually one of the things defined in a bandplan for each particular band radio band . It is essential in assuring that a transmission stays within its channel communications channel . An FM radio station , for example, must attenuate everything beyond 75 kHz from the center frequency by a few decibel s, and anything beyond 100 kHz the channel boundary by much more. Emissions on further adjacent channel s must be reduced to almost zero. FM broadcasting FM broadcast subcarrier s are normally required to stay under 75 kHz and up to 100 kHz if attenuation reduced to comply with the mask. The introduction of in band on channel IBOC digital radio in the United States has been slowed down by issues concerning the subcarriers it uses &ndash and the corresponding increase in the amount of energy in the sidebands &ndash overstepping the bounds of the spectral mask set forth for FM by the National Radio Systems Committee NRSC and enforce d by the Federal Communications Commission FCC . Other types of modulation have different spectral masks for the same purpose. Many digital modulation methods such as COFDM use the electromagnetic spectrum very efficiently, allowing for a very tight spectral mask. This allows placement of broadcast stations or other transmissions on channels right next to each other without ... more details
In telecommunications , spectral component is any of the wave s that range outside the interval of frequency frequencies assigned to a signal. Any waveform can be disassembled into its spectral components by Fourier analysis or Fourier transformation . The length of a pulse thereby is determined by its complex spectral components, which include not just their relative intensities, but also the relative positions spectral phase of these spectral components. See also Spectral width Bandwidth limited pulse Category Telecommunications engineering Telecomm term stub ... more details
Wrong way to begin. When taking the discrete Fourier transform DFT of a signal e.g. to obtain the spectral density power spectral density , spectral leakage will occur if any of the input signal s frequency components lie between reference frequencies. This results in a blurring of those components. Spectral leakage also occurs when the DFT is taken of a signal containing the remainder of a cycle. E.g. if a 3 Hertz sine wave is sampled for 0.9 seconds, a discontinuity results, which causes leakage. E.g. someone can write an example showing how a DFT blurs a sinusoid depending on how the sinusoid s frequency compares to the reference frequencies. Also, one can discuss how window function s affect spectral leakage. Can t redirect to a subtopic Window function Spectral analysis , or else I would be tempted. Image Spectral leakage from a sinusoid and rectangular window.png 350px right Spectral ..., which is spectral leakage. Thus, the spectral leakage is due to the finite frequency resolution ... 978 0 52152569 5, http books.google.com books?id OR SVjrcrLgC&pg PA164&dq spectral leakage p. 164 ... the same spectrum at different phases. That is, spectral leakage is a feature of the discrete Fourier ... real line as spectrum, while the discrete time Fourier transform has aliasing due to discrete but infinite samples it has continuous but periodic spectrum, but no spectral leakage. File Sinc function ... of the DTFT, spectral leakage is caused by the frequency response of the rectangular window its Fourier ... function Thus, to reduce the spectral leakage, one uses a window function with better frequency ... that there is no spectral leakage if one includes data points for infinite time. Instead of a delta ... the spectral energy is conserved, there is thus a trade off between these. Non rectangular .... Mathematics The mathematics of spectral leakage can be understood by computing the discrete Fourier ... k math relatively close to math xi math . Spectral leakage of a sinusoidal signal can be computed by breaking ... more details
orphan date December 2010 unreferenced date December 2010 Spectral purity is a quantification of the monochromaticity of a given light sample. This is a particularly important parameter in areas like laser operation and time measurement. Spectral purity is given by math Spectral purity frac triangle v v math Spectral purity is easier to achieve in devices that generate visible light visible and ultraviolet light, since higher frequency light results in greater spectral purity. Category Spectroscopy ... more details
A spectral envelope is a curve in the frequency amplitude plane, derived from a Fourier magnitude spectrum. It describes one point in time one window, to be precise . nofootnotes date December 2010 one source date December 2010 In remote sensing using a spectrometer , the spectral envelope of a feature is the boundary of its electromagnetic spectrum spectral properties, as defined by the range of brightness levels in each of the spectral bands of interest. References Swartz, Diemo 1998 . Spectral Envelopes . http recherche.ircam.fr anasyn schwarz da specenv 3 3Spectral Envelopes.html . http www.unesco.org csi pub source rs15.htm Category Spectroscopy ... more details
Infobox VG image File Spectral Gene cover.jpg 250px developer Idea Factory publisher Idea Factory designer engine series Spectral released vgrelease JP December 13, 2007 genre Tactical role playing game SRPG modes Single player video game Single player ratings platforms PlayStation 2 Spectral Gene is an Tactical role playing game SRPG for the PlayStation 2 , and is the next installment in Idea Factory s Spectral series. It was developed and published for Japan by Idea Factory and was released on December 13, 2007. It is unknown if it will ever be published outside of Japan. ref http www.gamefaqs.com console ps2 data 941627.html Spectral Gene Info Spectral Gene Information Spectral Gene Release Date Bot generated title ref References Reflist External links ja icon http www.ideaf.co.jp spectral gene index.html The official website of Spectral Gene Category 2007 video games Category Tactical role playing video games Category PlayStation 2 games Category PlayStation 2 only games Category Video games developed in Japan Category Japan exclusive video games tactical rpg videogame stub ... more details
. The Fourier transform on the real line is in one sense the spectral theory of derivative differentiation ...In mathematics , spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue ... A short course on spectral theory author William Arveson chapter Chapter 1 spectral theory and Banach ... ref The theory is connected to that of analytic functions because the spectral properties of an operator are related to analytic functions of the spectral parameter. ref name Sadovnichi cite book ... space the spectral theory of operators url http books.google.com books?id SR1QkG6OkVEC&pg PA181 ... The name spectral theory was introduced by David Hilbert in his original formulation of Hilbert space theory, which was cast in terms of quadratic form s in infinitely many variables. The original spectral ... , in an infinite dimensional setting. The later discovery in quantum mechanics that spectral theory ... three main ways to formulate spectral theory, all of which retain their usefulness. After Hilbert s initial formulation, the later development of abstract Hilbert space and the spectral theory of a single ... properties, and this is carried out by means of Pontryagin duality . One can also study the spectral ... spectral properties similar to that of Matrix mathematics matrices . Physical background The background ... pse maths research analysis research.html title Research at the analysis group ref Cquote Spectral ... Mawhin, p.4 and pp. 10 11. ref The later discovery in quantum mechanics that spectral theory could ... s spectral theory. A definition of spectrum main Spectrum functional analysis Consider a bounded ... of T in the complex plane. ref name Lorch Cite book title Spectral Theory author Edgar Raymond Lorch ... http books.google.com books?id X3U2AAAACAAJ&dq intitle spectral intitle theory inauthor Lorch&lr &as drrb ... 0758171560 url http books.google.com books?id X3U2AAAACAAJ&dq intitle spectral intitle theory inauthor ... of the Hilbert space Spectral theory spectra of transformations in a Hilbert space. In particular ... more details
In astronomy , the spectral index of a source is a measure of the dependence of radiative flux density on frequency . Given frequency math nu math and radiative flux math S math , the spectral index math alpha math is given implicitly by math S propto nu alpha. math Note that if flux does not follow a power law in frequency, the spectral index itself is a function of frequency. Rearranging the above, we see that the spectral index is given by math alpha frac partial log S partial log nu . math Spectral index is also sometimes defined in terms of wavelength math lambda math . In this case, the spectral index math alpha math is given implicitly by math S propto lambda n, math and at a given frequency, spectral index may be calculated by taking the derivative math alpha frac partial log S partial log lambda . math The opposite sign convention is sometimes employed, ref Burke, B.F., Graham Smith, F. 2009 . An Introduction to Radio Astronomy, 3rd Ed. , Cambridge University Press, Cambridge, UK, ISBN 9780521878081, page 132. ref in which the spectral index is given by math S propto nu alpha . math The spectral index of a source can hint at its properties. For example, using the positive sign convention, a spectral index of 0 to 2 at radio frequencies indicates thermal emission , while a steep negative spectral index typically indicates synchrotron emission . Spectral Index of Thermal emission At radio frequencies, where the Rayleigh Jeans law is a good approximation to the spectrum of thermal radiation, intensity is given by math B nu T frac 2 nu 2 k T c 2 . math Taking the logarithm ... partial log B nu T partial log nu 2. math Using the positive sign convention, the spectral index of thermal radiation is thus math alpha approx 2 math in the Raleigh Jeans regime. The spectral index ... Jeans regime, the radio spectral index is defined as ref cite web title Radio Spectral Index publisher ... stub es ndice espectral fr Indice spectral it Indice spettrale ... more details
In mathematics, the spectral gap is the difference between the moduli of the two largest eigenvalue s of a matrix or operator alternately, it is sometimes taken as the smallest non zero eigenvalue. Various theorems relate this difference to other properties of the system. See Expander graph discrete case Poincar inequality continuous case See also Spectral radius Eigengap disambig Category Mathematical disambiguation Category Spectral theory ... more details
In mathematics , the spectral abscissa of a matrix mathematics matrix or a bounded linear operator is the supremum among the real part of the elements in its spectrum of a matrix spectrum , sometines denoted as math eta A math Matrices Let sub 1 sub , ..., sub s sub be the real number real or complex number complex eigenvalues of a matrix A C sup n n sup . Then its spectral abscissa is defined as math eta A max i rm Re lambda i , math It is often used as a measure of stability in control theory, where a continuous system is stable iF all its eigenvalues are located in the left half plane, i.e. math eta A 0 math See also Spectral radius DEFAULTSORT Spectral Abscissa Category Spectral theory Category Matrix theory mathematics stub ... more details
Unreferenced stub auto yes date December 2009 File Spectrum of blue sky.svg thumb 300px right Spectrum of blue sky Spectral Signatures are the specific combination of reflected and absorbed electromagnetic radiation electromagnetic EM radiation at varying wavelengths which can uniquely identify an object. The spectral signature of stars indicates the spectrum according to the EM spectrum. The spectral signature of an object is a function of the incidental EM wavelength and material interaction with that section of the electromagnetic spectrum . The measurements can be made with various instruments, including a task specific spectrometer , although the most common method is separation of the Red, Green, Blue and Near Infrared portion of the EM spectrum as acquired by digital cameras. Calibration of spectral signatures under specific illumination are collected in order to apply an empirical correction to airborne or satellite imagery digital images. When using a spectrometer, you will look through it at a tube of gas with high voltages passing through it. In the Spectrometer, you will be able to see specific rays of colour falling on graduations on the inside. Each substance will have its own unique falling of rays. Most remote sensing applications process digital images to extract spectral signature at each pixel and use such signature to divide the image in groups of similar pixels segmentation using different approaches, and, as last step, assign a class to each group classification by comparing with known spectral signatures. Depending on pixel resolution, a pixel can represent many spectral signature mixed together that is why a lot of remote sensing analysis is done to unmix mixtures . Ultimately correct matching of spectral signature recorded by image pixel with spectral signature of existing elements leads to accurate classification in remote sensing. DEFAULTSORT Spectral Signature Category Spectroscopy Sci stub ca Signatura espectral es Firma espectral id Cir ... more details
In mathematics and physics , the spectral asymmetry is the asymmetry in the distribution of the spectrum of eigenvalue s of an Operator mathematics operator . In mathematics, the spectral asymmetry arises in the study of elliptic operator s on compact manifold s, and is given a deep meaning by the Atiyah Singer index theorem . In physics, it has numerous applications, typically resulting in a fractional charge physics charge due to the asymmetry of the spectrum of a Dirac operator . For example, the vacuum expectation value of the baryon number is given by the spectral asymmetry of the Hamiltonian operator . The spectral asymmetry of the confined quark fields is an important property of the chiral bag model . Definition Given an operator with eigenvalue s math omega n math , an equal number of which are positive and negative, the spectral asymmetry may be defined as the sum math B lim t to 0 frac 1 2 sum n sgn omega n exp t omega n math where math sgn x math is the sign function . Other regularization physics regulator s, such as the zeta function regulator , may be used. The need for both a positive and negative spectrum in the definition is why the spectral asymmetry usually occurs in the study of Dirac operator s. Example As an example, consider an operator with a spectrum math omega n n theta math where n is an integer, ranging over all positive and negative values. One may show in a straightforward manner that the spectral asymmetry in this case is math B theta math . Discussion Related to the spectral asymmetry is the vacuum expectation value of the energy associated with the operator, the Casimir energy , which is given by math E lim t to 0 frac 1 2 sum n omega n exp t omega n math This sum is formally divergent, and the divergences must be accounted for and removed using standard regularization techniques. References MF Atiyah, VK Patodi and IM Singer, Spectral ... 1990 p. 109 143. Category Spectral theory ... more details
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