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Topic: Discrete spectrum

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	CommsDesign - Discrete Spectrum Techniques for Spectral Regrowth Analysis
		However, compared to the generally correct continuous-spectrum description, the discrete spectrum approach introduces errors in both output bandwidth estimation and in power estimation of the spectral regrowth.
		In this figure, the input is consists of the sum of three cosine signals, which results in a discrete input-frequency spectrum with components at the input frequencies.
		is the frequency resolution in the discrete spectrum approximation.
	www.commsdesign.com /showArticle.jhtml?articleID=192200559 (1337 words)

	Spectral density - Wikipedia, the free encyclopedia
		The spectrum analyzer measures essentially the magnitude of the short-time Fourier transform (STFT) of an input signal.
		The spectrum of a light source is a measure of the power carried by each frequency or "color" in a light source.
		The light spectrum is usually measured at points (often 31) along the visible spectrum, in wavelength space instead of frequency space, which makes it not strictly a spectral density.
	en.wikipedia.org /wiki/Power_spectrum (1026 words)

	Dynamic bit allocation subband excited transform coding method and apparatus - Patent 5235671
		As in that approach, a discrete transform of a window of speech is performed to generate a discrete spectrum of coefficients.
		To that end, the spectrum is partitioned into L contiguous subbands and a spectral envelope estimate is based on a piecewise constant approximation of those subbands at 22.
		This flattening of the spectrum is equivalent to inverse filtering the signal based on the piecewise-constant estimate of the spectral envelope.
	www.freepatentsonline.com /5235671.html (4710 words)

	Electromagnetic Radiation
		The continuous spectrum from these kinds of objects is also called a thermal spectrum, because hot, dense objects will emit electromagnetic radiation at all wavelengths or colors.
		A thermal spectrum is the simplest type of spectrum because its shape depends on only the temperature.
		A ``flbody'' is an object that absorbs all the light falling on it, reflecting none of it, hence, it appears fl.
	www.astronomynotes.com /light/s4.htm (740 words)

	The Reference Frame: Discrete physics
		The discrete social security number is only a good description of a person for those who are not interested about anything else connected with the person.
		Try to look for discrete objects and choices that are used in our current laws of physics and string theory in particular; they must be explained by a deeper principle that is inherently continuous and geometric, where the word "geometry" is used in a generalized sense.
		The Discrete Universe is one of the postmodern religions.
	motls.blogspot.com /2005/11/discrete-physics.html (6274 words)

	Spectrum
		The spectrum of a sound is a primary determinant of its perceived
		A partial spectrum is also known as a line spectrum, where discrete frequencies are present.
		Analyzing the spectrum of a sound is a way of understanding its behaviour in the frequency domain, as opposed to its behaviour in the time domain, according to its
	www.sfu.ca /sonic-studio/handbook/Spectrum.html (282 words)

	Taxonomy of spectra
		Part (a) of the figure shows the spectrum of a harmonic signal, which is a periodic signal whose fundamental frequency is in the range of perceptible pitches, roughly between 50 and 4000 Hertz.
		In a harmonic signal, the power shown in the spectrum is concentrated on a discrete subset of the frequency axis (a discrete set consists of isolated points, only finitely many in any bounded interval).
		For discrete spectra, the pitch is primarily encoded in the frequencies of the partials.
	www-crca.ucsd.edu /~msp/techniques/latest/book-html/node76.html (764 words)

	[No title]
		Discrete G-spectra are considered in more detail in [3], which shows (see [3, Theorem 3.6]) that SptG is a model category, where a morphism f in SptG is a weak equivalence (cofibration) if and only if f is a weak equivalence (cofibrat* *ion) in Spt, the category of spectra.
		The p* ro- discrete* cochain complex is a complex of abelian groups or spectra, respectivel* y, and the limit and colimit are both formed in abelian groups or spectra, respect *ively.
		The homotopy fixed point spectrum is defined with respect to a continuo* us action of G on the spectrum*.
	hopf.math.purdue.edu /DavisDaniel/cplx2.txt (2217 words)

	Colour and the Electromagnetic Spectrum
		If light which normally produces a continuous spectrum is passed through a gas or vapour, certain frequencies are absorbed and are found to be absent from the spectrum.
		The frequencies of light present in the discrete emission spectrum of a vapour corresponds with those frequencies which are missing in the absorption spectrum of the vapour.
		Different parts of the spectrum are given different names, for example: radio waves, infrared, visible light, ultraviolet, X-rays and gamma rays.
	www.physchem.co.za /Light/Spectrum.htm (832 words)

	wavepatterns and harmonics (Site not responding. Last check: 2007-09-17)
		discrete spectrum does not contradict the wave theory of light (might not be obvious to everyone)).
		If what I believe is correct, the most fundamental discrete spectrum is simply a result of the simplest oscillating motion.
		Hydr0matic -- You are correct that there's nothing in the wave theory of light that precludes discrete spectra -- think for a moment about the actual quantum theory of radiation -- based on Maxwell's equations, which in first order QM perturbation theory is virtually identical to classical EandM.
	www.physicsforums.com /showthread.php?p=419753 (1707 words)

	What is known about the character of noise created by submarines? Appendix 1 - The Future of Russia's Strategic Nuclear ...
		Moreover, the aggregate of the discrete components of the noise spectrum (the so called "acoustic portrait") which is unique for each submarine, may be used to identify the source.
		Discrete lines in the frequency band of several Hz to several hundred Hertz is associated with vibrations from the submarine's hull and power plant equipment.
		The most characteristic line in the SL spectrum is the peak at frequencies of 50 and 60 Hz for Russian and American submarines respectively, i.e., the lines which correspond to the basic frequencies of the submarines electric generators.
	www.fas.org /spp/eprint/snf03221.htm (2733 words)

	CMB - Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type
		We describe procedures for checking when these systems have pure discrete spectrum (the ``balanced pairs algorithm'' and the ``overlap algorithm'') and study the relation between them.
		In particular, we show that pure discrete spectrum for the $\mathbb{R}$-action implies pure discrete spectrum for the $\mathbb{Z}$-action, and obtain a partial result in the other direction.
		As a corollary, we prove pure discrete spectrum for every $\mathbb{R}$-action associated with a two-symbol substitution of Pisot type (this is conjectured for an arbitrary number of symbols).
	journals.cms.math.ca /cgi-bin/vault/view/sirventRVM8242 (149 words)

	Narrow Pulse System Characterization (Site not responding. Last check: 2007-09-17)
		The theoretically derived power spectrum can be used to calculate the mean power in the bandwidth of a narrowband victim RF receiver at its operating or center frequency, and hence provides important information regarding the interference potential.
		The discrete spectrum is not a factor for RF frequencies above a few hundred MHz.
		For narrowband victim receivers where gains due to the UWB transmitter filters/antenna, propagation channel, and receiver are fairly constant over the receiver bandwidth, the received interference power can easily be calculated by applying the appropriate gain factors to the power in the receiver bandwidth at the center frequency of the receiver.
	www.its.bldrdoc.gov /tpr/2000/its_t/narrow_pulse/narrow_pulse.html (775 words)

	VQM Programs - Spectroscopy Lab Suite
		The Gas Lamps module presents the relationship between the discrete energy levels in a gas and the spectrum of the light emitted by a gas discharge tube.
		The LED module extends the idea of the spectrum of the emitted light to from gas discharge tubes, which have a discrete spectrum resulting from a discrete set of allowed energy levels, to the continuous spectrum of an LED which result from an energy band.
		Observe the relationship between the energy band gap of an LED and the spectrum of the emitted light for a range of different LEDs.
	web.phys.ksu.edu /vqm/software/descript/sls.html (695 words)

	[No title]
		The discrete signal x(nT) of sampling corresponds to the coefficients of the complex Fourier series expansion (Discrete Spectrum) Cn.
		From the above equation, we understand that the spectrum of the sampled signal is a periodic signal and the period is 1/T. Thus, sampled discrete aperiodic signal has continuous periodic spectrum.
		Usually the unit of period is t(time) but for spectrum, since the same spectrum repeats at an interval of -fs/2〜fs/2, the period of spectrum is -fs/2〜fs/2.
	laputa.cs.shinshu-u.ac.jp /~tariq/sampling-and-spectrum/sampling-and-spectrum.htm (1132 words)

	Discrete Fourier Transform
		Discrete Fourier Transform (DFT) is used extensively in signal processing applications such as communications, broadcasting, entertainment and many other areas.
		Since sampling is multiplication of x(t) with sampling signal s(t) in time domain, it results in the convolution of the signal spectrum with the spectrum of s(t), which is a series of harmonics of Ƥs as shown in Figure 6(b).
		Thus, we consider one period of the final discrete spectrum as the discrete Fourier transform of one period of the discrete periodic signal.
	rfdesign.com /mag/radio_understanding_discrete_fourier (2020 words)

	ILL : ANNUAL REPORT 2001
		In the case of matter waves, the splitting of the frequency line is equivalent to a discrete spectrum of the particles energy.
		Equations (2) and (3) show that due to the modulator, the transmitted state is a superposition of coherent waves with a discrete frequency spectrum.
		As proposed earlier [2], the primary neutron monochromatisation of UCN as well as the analysis of the diffracted spectrum were performed by means of Neutron Interference Filters [3,4] (NIF), a quantum device, which is analogous to the Fabry-Perot interferometer for light.
	www.ill.fr /AR-01/p-80.htm (1391 words)

	Light Sources Tutorial - Line Sources (Site not responding. Last check: 2007-09-17)
		The spectrum obtained by passing this light through a prism or grating is show in the next image.
		Each color is located at the same position in the picture as it was in the continuous spectrum, but most of the image is dark because hydrogen emits light of only a few colors.
		This is called a line spectrum or a discrete spectrum because of the individual, discrete, bands of color.
	www.assumption.edu /users/bniece/Spectra/Tutorials/LS_Line.html (300 words)

	Chapter 11: The Fourier Transform
		The methods of Fourier analysis described in previous chapters have as their domain three classes of functions: discrete data vectors with finite number of values, discrete vectors with infinite number of values, and continuous functions which are confined to a finite interval.
		Previously, the frequency spectrum was conceived as a discrete "stem" plot with the height of each stem representing the Fourier coefficients.
		Now, the spectrum is a "stairs" plot in which the area of each stair step represents the Fourier coefficients.
	research.opt.indiana.edu /Library/FourierBook/ch11.html (1590 words)

	THE BOHR ATOM: ABSORPTION SPECTRUM (Site not responding. Last check: 2007-09-17)
		The Bohr Model of the Atom (or Modified Solar System Model): That model of the atom which succeeded the Rutherford Model of the Atom when it was unable to account for the discrete spectrum of light emitted by atoms.
		Discrete: Separate or individually distinct, consisting of distinct parts or discontinuous elements.
		In the atom shown, there are only three discrete possible orbits and three discrete possible electron energies to go with them.
	einstein.byu.edu /~masong/HTMstuff/C15A2.html (518 words)

	Single, Double, Multiple Source Interference
		Two German scientists, Robert Bunsen (a chemist) and Gustav Kirchhoff (a physicist), showed that the dark lines in the spectrum of sunlight corresponded to the bright lines of excited elements seen in laboratories on the earth.
		Helium was discovered in 1868 by J. Norman Lockyear in the spectrum of a solar eclipse.
		The French astronomer Pierre Janssen (1824-1907) discovered helium in the spectrum of the corona of the sun during an eclipse in 1868.
	hypertextbook.com /physics/waves/interference-light (174 words)

	Historical Notes: History [of quantum theory]
		But in 1900 Max Planck noticed that fits to the measured spectrum of electromagnetic radiation produced by hot objects could be explained if there were discrete quanta of electromagnetic energy.
		And by 1910 work by Albert Einstein, notably on the photoelectric effect and on heat capacities of solids, had given evidence for discrete quanta of energy in both light and matter.
		In 1913 Niels Bohr then made the suggestion that the discrete spectrum of light emitted by hydrogen atoms could be explained as being produced by electrons making transitions between orbits with discrete quantized angular momenta.
	www.wolframscience.com /reference/notes/1056a (2138 words)

	Restriction of square integrable representations: Discrete spectrum, Bent Ørsted, Jorge Vargas
		In this paper, we study the problem of restricting a square integrable representation of a connected semisimple Lie group to a reductive subgroup.
		Using a geometric method of restricting sections of a vector bundle to a submanifold, we obtain information about both the discrete and the continuous spectrum.
		[15] —, Discrete decomposability of the restriction of $A_\mathfrak q(\lambda)$ with respect to reductive subgroups, II: Micro-local analysis and asymptotic $K$-support, Ann.
	projecteuclid.org /getRecord?id=euclid.dmj/1086957717 (693 words)

	Room Temperature Atomic discrete emission Spectra from Solids
		Considered an excited atom, the electromagnetic spectrum can be redefined arranging these four radiations one after another as energy spectrum.
		The above spectrum is an artistic view of Rb X-rays, Bharat radiation higher than that of UV with energy in eV level, and UV dominant atomic spectrum from a single Rb XRF source.
		In practice, expected is a discrete atomic emission line spectrum having more lines in UV range.
	www.geocities.com /raomap/discovery5.html (1742 words)

	Discrete-Time Fourier Series
		vs k is called the phase spectrum of x[n].
		These plots, particularly the magnitude spectrum, provide a picture of the frequency composition of the signal.
		Only one period of the signal and one repetition of the spectra are shown.
	www.jhu.edu /~signals/discretefourier/index.htm (468 words)

	THE CHEMICAL DETECTIVE
		Have students identify the colors present in the spectrum; explain that there is no set number of colors in the spectrum, but that it is a continuous range of colors.
		Next have them view a source which produces a discrete spectrum (gas tube, "fl light") and have them explain how the spectrum they see is different.
		The viewing of a spectrum- a rainbow of colors- is always a memorable experience; it is also a vivid example of light's wave-like properties.
	fuse.pha.jhu.edu /outreach/kit1/detective.html (986 words)

	Sampling and Reconstruction of Periodic Signals \| DSP-FPGA.com
		The continuous analog data must be sampled at discrete intervals that are carefully chosen to insure an accurate representation of the original analog signal.
		Figure 4(a) represents the continuous spectrum of the resulted signal while 4(b) represents the discrete spectrum of the same signal, sampled at 32KHz.
		However we have to know where the signal of interest is located in the spectrum and apply a specific band pass filter to get rid of all the aliasing introduced by process of digitizing the analog signal.
	www.dsp-fpga.com /articles/neagoe_and_fugerer (3245 words)

	Understanding digital signal processing's frequency domain
		Understanding the differences between analog and discrete spectra is one of the reasons DSP has the reputation for being difficult to learn.
		First, the notion that the spectrum of the discrete x(n) sequence is an infinite set of spectral impulses does not imply that x(n) has infinite energy.
		For discrete signals, frequency is measured in radians/sample.” Redrawing the spectrum from Figure 11(b) illustrates the normalized angle and normalized frequency axis representations in Figure 13.
	rfdesign.com /mag/radio_understanding_digital_signal (3825 words)

	Oleg Safronov's homepage
		[1] Safronov, O.L: The discrete spectrum in the spectral gaps of
		[6] Safronov, Oleg: The discrete spectrum of the perturbed periodic
		[7] Safronov, O.L.: The discrete spectrum in the gaps of the continuous
	www.math.uab.edu /oleg/publications.htm (279 words)

	Discrete spectrum of many-body Schrödinger operators with non-constant magnetic fields. I, Tetsuya Hattori
		Discrete spectrum of many-body Schrödinger operators with non-constant magnetic fields.
		[18] G. Zhislin, On the finiteness of the discrete spectrum of the energy operator of negative ions, Theor.
		[19] G. Zhislin, Finiteness of the discrete spectrum in the quantum N-particle prob- lem, Theor.
	projecteuclid.org /getRecord?id=euclid.nmj/1118771746 (420 words)

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