In mathematics , particularly linear algebra and functional analysis , the spectraltheorem is any of a number of results about linear operator s or about matrix mathematics matrices . In broad terms the spectral ... s, which are as simple as one can hope to find. In more abstract language, the spectraltheorem is a statement ... of operators to which the spectraltheorem applies are self adjoint operator s or more generally normal operator s on Hilbert space s. The spectraltheorem also provides a canonical form canonical ... we consider mainly the simplest kind of spectraltheorem, that for a self adjoint operator on a Hilbert space. However, as noted above, the spectraltheorem also holds for normal operators ... induction then finishes the proof. The spectraltheorem holds also for symmetric maps on finite ... decomposition and the singular value decomposition . Normal matrices The spectraltheorem extends to a more ..., the statement of the spectraltheorem for compact operator compact self adjoint operators is virtually ... of eigenvalues. The above spectraltheorem holds for real or complex Hilbert spaces. If the compactness ... self adjoint operators See also Eigenfunction Self adjoint operator Spectraltheorem The next generalization ... measure spectral measure spectral measure . There is also an analogous spectraltheorem for bounded ... be complex valued. An alternative formulation of the spectraltheorem expresses the operator math ... the normal operator in question is compact operator compact , this version of the spectraltheorem reduces to the finite dimensional spectraltheorem above, except that the operator is expressed as a linear ... , are unbounded. There is also a spectraltheorem for self adjoint operator s that applies in these cases ... . In general, spectraltheorem for self adjoint operators may take several equivalent forms. Spectraltheorem in the form of multiplication operator . For each self adjoint operator T acting in a Hilbert ... decomposition is a special case. Singular value decomposition , a generalisation of spectraltheorem ... more details
In mathematics , the Freudenthal spectraltheorem is a result in Riesz space Riesz space theory proved by Hans Freudenthal in 1936. It roughly states that any element dominated by a positive element in a Riesz space with the Riesz space Projection properties principle projection property can in a sense be approximated uniformly by simple function s. Numerous well known results may be derived from the Freudenthal spectraltheorem. The well known Radon Nikodym theorem , the validity of the Poisson kernel Poisson formula and the Spectraltheorem from normal operator s can all be shown to follow as a special cases of the Freudenthal spectraltheorem. Statement Let e be any positive element in a Riesz space E . A positive element of p in E is called a component of e if math p wedge e p 0 math . If math p 1,p 2, ldots,p n math are pairwise Riesz space Disjoint complements disjoint components of e , any real linear combination of math p 1,p 2, ldots,p n math is called an e simple function. The Freudenthal spectraltheorem states Let E be any Riesz space with the principle projection property and e any positive element in E . Then for any element f in the principle ideal generated by f , there exist sequences math s n math and math t n math of e simple functions, such that math s n math is monotone increasing and converges Riesz space Order convergence e uniformly to f , and math t n math is monotone decreasing and converges e uniformly to f . Relation to the Radon Nikodym theorem Let math X, Sigma math be a measure space and math M sigma math the real space of signed measure The space ... . Moreover, since by the Freudenthal spectraltheorem, any measure math nu math in the Riesz space ... mu math measurable simple functions on math X, Sigma math , by Lebesgue monotone convergence theorem Lebesgue s monotone convergence theorem Lebesgue s monotone convergence theorem math nu math can ... math . See also Radon Nikodym theorem References Citation last Zaanen first Adriaan C. year 1996 title ... 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
theorem . An often more useful alternative is the power spectral density PSD , which describes ... of Fourier analysis is Parseval s theorem which states that the area under the energy spectral ...refimprove date May 2008 Merge from Spectral energy distribution discuss Talk Spectral energy distribution date September 2010 In statistical signal processing and physics , the spectral density , power spectral density PSD , or energy spectral density ESD , is a positive real function of a frequency ... simply the spectrum of the signal. Intuitively, the spectral density measures the frequency content ... a wave, such as an electromagnetic wave , random vibration , or an sound wave acoustic wave . The spectral ... power carried by the wave, per unit frequency, known as the power spectral density PSD of the signal. Power spectral density is commonly expressed in watt s per hertz W Hz ref cite book title VSAT ... books?id CMx5HQ1Mr UC&pg PR20&dq 22power spectral density 22 W Hz&lr &as brr 0&ei VYwvSImyA4L4sQPxxJXzAg ... books.google.com books?id jDeRCSqtev4C&pg PA352&dq 22power spectral density 22 22energy spectral ... spectral density. ref cite book title Reliability Engineering author Alessandro Birolini publisher ...&pg PA83&dq acceleration spectral density g hz&as brr 3&ei q24xSpKOBZXkzASPrs39BQ ref Although it is not necessary ... the terms used will assume that the signal varies in time. Definition Energy spectral density Anchor energy spectral density The energy spectral density describes how the Energy signal processing ... energy integrable function square integrable signal, the spectral density math Phi omega math ... still have an energy spectral density math Phi omega left frac 1 sqrt 2 pi sum n infty infty f n ... an energy spectral density per se , but the sequence can be treated as periodic, using a Discrete Fourier Transform DFT to make a discrete spectrum, or it can be extended with zeros and a spectral density can be computed as in the infinite sequence case. The continuous and discrete spectral densities ... more details
In noncommutative geometry and related branches of mathematics and mathematical physics , a spectral triple is a set of data which encodes geometric phenomenon in an analytic way. The definition typically involves a Hilbert space , an algebra ring theory algebra of operators on it and an unbounded self adjoint operator, endowed with supplemental structures. It was conceived by Alain Connes who was motivated by the Atiyah Singer index theorem and sought its extension to noncommutative spaces. Some authors refer to this notion as unbounded K homology K cycles or as unbounded Fredholm modules . Motivation A motivating example of spectral triple is given by the algebra of functions on a compact spin ... the smooth structure, which is Connes reconstruction theorem, but I think this result is too recent ... part of the index theorem , while the geometric local side involves the Dixmier trace and commutators ... of the index theorem . Extensions of the index theorem can be considered in cases, typically when one .... Definition An odd spectral triple is a triple A, H, D consisting of a Hilbert space H, an algebra ... D satisfying nowiki a, D &infin nowiki for any a &isin A. An even spectral triple is an odd spectral ... to this grading. One could also say that an even spectral triple is given by a quartet A, H, D, &gamma ... &gamma &gamma D. A finitely summable spectral triple is a spectral triple A, H, D such that a.D ... H . When this condition is satisfied, the triple A, H, D is said to be p summable . A spectral triple ... connes94 Let &delta T denote the commutator of D with an operator T on H. A spectral triple is said ... of the iterates &delta sup n sup of &delta . When a spectral triple A, H, D is p summable ... the dimension spectrum of A, H, D . A real spectral triple is a spectral triple A, H, D accompanied ... Given a spectral triple A, H, D , one can apply several important operations to it. The most fundamental ... from K sub 1 sub A to Z . When the spectral triple is finitely summable, one may write the above ... more details
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 bit symbol , which is equivalent ... modulation rate or line code pulse rate. Link spectral efficiency is typically used to analyse the efficiency ... of 3,400 300 3,100 hertz. The spectral efficiency or modulation efficiency is 56,000 3,100 18.1 ... 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 efficiency ... 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 efficiency ... 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 reduces ... bound for the spectral efficiency possible without bit error s in a channel with a certain SNR, if ideal error coding and modulation is assumed, is given by the Shannon Hartley theorem . Example 7 If the SNR is 1 times expressed as a ratio, corresponding to 0 decibel , the link spectral efficiency ... efficiently compressed. The link spectral efficiency of a wireless telephony link may ..., 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 efficiency ... and forward error correction reduce the spectral efficiency in bit s Hz but substantially lower ... more details
, the following theorem holds Theorem Let A C sup n n sup be a complex valued matrix and A its spectral ...In mathematics , the spectral radius of a matrix mathematics square matrix or a bounded linear operator ... or complex number complex eigenvalues of a matrix A C sup n n sup . Then its spectral radius A is defined ... yet useful upper bound for the spectral radius of a matrix Lemma Let A C sup n n sup be a complex valued matrix, A its spectral radius and a matrix norm Consistent norms consistent matrix norm ... math lambda k leq A k math and therefore math rho A leq A k 1 k , , square math The spectral radius ... lim k to infty A k 0 right math From the Jordan normal form theorem, we know that for any ... part of the statement. math square math Theorem Gelfand s formula, 1941 For any matrix norm , we have math rho A lim k to infty A k 1 k . math In other words, the Gelfand s formula shows how the spectral ... theorem, math lim k to infty tilde A k 0. math That means, by the sequence limit definition ... A. math Then, obviously, math rho check A frac rho A rho A epsilon 1 math and so, by the previous theorem ... lim k to infty A k 1 k rho A . , , square math Gelfand s formula leads directly to a bound on the spectral ..., we can replace in the limit definition the left lower bound with the spectral radius itself and write ... eigenvalues are 5, 10, 10 by definition, its spectral radius is A 10. In the following table, the values ... operator if its spectral radius coincides with its numerical radius . An example of such an operator is a normal operator . Graphs The spectral radius of a finite graph mathematics graph is defined to be the spectral radius of its adjacency matrix . This definition extends to the case of infinite ... math , i.e., math gamma f v sum u,v in E G f u math . The spectral radius of G is defined to be the spectral radius of the bounded linear operator math gamma math . See also Spectral gap The Joint spectral radius is a generalization of the spectral radius to sets of matrices. Category Spectral theory ... 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
Merge Spectral element method date October 2009 Spectral methods are a class of techniques used in applied ... the use of the Fast Fourier Transform . Where applicable, spectral methods have excellent error properties, with the so called exponential convergence being the fastest possible. Spectral methods ... to, Fourier series methods for periodic geometry problems, polynomial spectral methods for finite and unbounded geometry problems, pseudospectral methods for highly nonlinear problems, and spectral ... for computing solutions to these PDEs. In a typical case, spectral methods take advantage ... to solve those ODEs. The spectral method and the finite element method are closely related and built on the same ideas the main difference between them is that the spectral method approximates the solution ... of this, the spectral method takes on a global approach while the finite element method is a local approach . This is part of why the spectral method works best when the solution is Smooth function smooth . In fact there are no known three dimensional single domain spectral shock capturing results. ref name CHQZ http books.google.com books?id 7COgEw5 EBQC pp 235, Spectral Methods evolution ... high or increases as the grid parameter h decreases to zero is sometimes called a spectral element method . The implementation of the spectral method is normally accomplished either with collocation method collocation or a Galerkin method Galerkin or a Tau method Tau approach. Examples of spectral ... if we assume for instance that f has a continuous second derivative. By the uniqueness theorem for Fourier ... equation using a spectral approach. Given math u x,0 math on the periodic domain math x in left 0,2 ... et al. for more details. A relationship with the spectral element method One can show that if math ... math . We say that the spectral method is of order math n math , for every n 0. Because a spectral ... properties. However, whereas the spectral method is based on the eigendecomposition of the particular ... more details
, roughly speaking? Main Spectraltheorem See also Eigenvalue, eigenvector and eigenspace In functional analysis and linear algebra the spectraltheorem establishes conditions under which an operator ...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 spectraltheorem was therefore conceived as a version of the theorem on principal axes of an ellipsoid , 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 ... with Fourier analysis . The Fourier transform on the real line is in one sense the spectral theory ... also study the spectral properties of operators on Banach spaces . For example, compact operator s on Banach spaces have many spectral properties similar to that of Matrix mathematics matrices . Physical ... ref Cquote Spectral theory is connected with the investigation of localized vibrations of a variety ... discovery in quantum mechanics that spectral theory could explain features of atomic spectra was therefore fortuitous, rather than being an object of Hilbert s spectral theory. A definition of spectrum ... Cite book title Spectral Theory author Edgar Raymond Lorch year 2003 edition Reprint of Oxford 1962 ... 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
Unreferenced stub auto yes date December 2009 Spectral imaging is a branch of spectroscopy and of photography in which a complete spectrum or some spectral information such as the Doppler shift or Zeeman splitting of a spectral line 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 . Various distinctions among techniques are applied, based on criteria including spectral range, spectral resolution, number of bands, width and contiguousness of bands, and application. The terms include multispectral imaging , hyperspectral imaging , full spectral imaging , imaging spectroscopy or chemical imaging . These terms are seldom applied to the use of only Tetrachromacy four or Pentachromacy five bands that are all within the visible light range. Spectral images are often represented as an image cube, a type of data cube . See also Dopplergraph Imaging spectrometer DEFAULTSORT Spectral Imaging Category Astronomical spectroscopy Physics stub ar ... 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
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 Timbre Category Spectroscopy ... 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 eigenvalue s and eigenvector s 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 spectral line , edges, and various physical processes producing continuum shapes disambig ... 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 Linear algebra stub ... more details
In mathematics, the spectral gap is the difference between the absolute value 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
cleanup date April 2011 lead too short date April 2011 Spectral Networks is deploying a WiMAX network in Southern Iowa and Northern Missouri . ref Reference 1 ref References ref cite web title Spectral Networks Website url http www.spectralnetworks.net publisher Source ref Reflist External links Spectral Networks http www.spectralnetworks.net Categories Category Articles created via the Article Wizard Category Telecommunications companies of the United States ... more details
In telecommunication s, spectral width is the wavelength interval over which the magnitude of all spectral component s is equal to or greater than a specified fraction of the magnitude of the component having the maximum value. In optical Telecommunication communications applications, the usual method of specifying spectral width is the full width at half maximum . This is the same convention used in Bandwidth signal processing bandwidth , defined as the frequency range where power drops by less than half at most &minus 3 dB . The FWHM method may be difficult to apply when the spectrum has a complex shape. Another method of specifying spectral width is a special case of Root mean square root mean square deviation where the independent variable is wavelength, , and f is a suitable radiometric quantity. The relative spectral width , , is frequently used where is obtained according to note 1, and is the center wavelength. See also Spectral linewidth in optics References Refimprove date January 2009 references FS1037C MS188 Category Telecommunications terms telecomm term stub fr Largeur de bande ... 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 left nu right frac partial log S left nu right 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 alpha, math and at a given frequency, spectral index may be calculated by taking the derivative math alpha left lambda right frac partial log S left lambda right 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 i.e. in the low frequency, long wavelength limit , where the Rayleigh Jeans law is a good approximation ... convention, the spectral index of thermal radiation is thus math alpha simeq 2 math in the Rayleigh Jeans regime. The spectral index departs from this value at shorter wavelengths, for which the Rayleigh ... regime, the radio spectral index is defined implicitly by ref cite web title Radio Spectral Index ... stub es ndice espectral fr Indice spectral it Indice spettrale ... 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 image processing 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 espec ... more details
Infobox Album See Wikipedia WikiProject Albums Name Spectral Worship Type Album Artist Guv ner Cover Background Released 1998 Recorded Genre Indie rock Length Label Merge Records Producer Nicolas Vernhes and Charles Gansa Reviews Pitchfork Media 7.8 10 http www.pitchforkmedia.com article record review 18255 spectral worship link Last album The Hunt Guv ner album The Hunt br 1996 This album Spectral Worship br 1998 Next album Spectral Worship is an album by the American indie band Guv ner . It was released by Merge Records in 1998. The album features a cover of Jealous Guy by John Lennon , re titled Jealous Girl as it is sung by Pumpkin Wentzel. Track listing Spectral Worship Chereza Love the Lamp Wounded Birds and Vampires own the Edge Anaphelact Coozwax Jealous Girl small Lennon small Time Rarely Stands Still Anything Difficulty in Openness Someone Else Spectral Workshop Welcome Instrumentation and Personnel Charles Gansa guitar , Singing vocals Pumpkin Wentzel Bass guitar bass , vocals Danny Tunick Drum kit drums Cindy Greene whistling Nicky Furnace backing vocals, handclaps So Yong Kim tongue claps Michael Rohatyn vocals External links http www.mergerecords.com catalog.php?method band&query band id 40& Spectral Worship on MergeRecords.com Category 1998 albums Category Merge Records albums ... more details
Unreferenced date December 2009 The spectral linewidth characterizes the width of a spectral line , 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 Spectral line 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 ru tr Spektral izgi geni li i uk ... more details
Multiple issues orphan August 2008 unreferenced June 2008 context February 2009 Spectral mutability is a desired capability Clarify date August 2008 where RF system s have the appropriate mix of both manual and automatic flexibility and agility to affect all aspects of their operating parameters e.g. waveform , Bandwidth signal processing bandwidth , power, frequency , direction and maximize efficiency of spectral use and maintain optimum compatibility between systems. Category Radio technology electromagnetism stub ... more details
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