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# Topic: Spectral density

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 Spectral density - Wikipedia, the free encyclopedia In applied mathematics and physics, the spectral density is a general concept applied to a signal which may have any physical dimensions or none at all. The spectral centroid of a signal is the midpoint of its spectral density function, i.e. The power spectral density of a light source is a measure of the power carried by each frequency or "color" in a light source. en.wikipedia.org /wiki/Spectral_power_distribution   (940 words)

 Porges and Bohrer (1991) Spectral analysis provides a method to extract information about periodicities, even when they are embedded in a complex pattern and may represent only a small proportion of the total variance of the time series. Cross- spectral analysis is the appropriate frequency domain method of assessing the covariation of respiration and heart period at the breathing frequencies. For spectral analysis to appropriately function it is necessary that the data are stationary and that the data are not aliased. www.wam.umd.edu /~sporges/bohrer/bohrer4.htm   (4614 words)

 [Spectral power density and coherence in sleep EEG in patients with acquired immunodeficiency syndrome] Spectral characteristics of elementary EEG-epochs of 40 s length were computed, and sleep staging was performed visually for these intervals. The spectral power density of eight EEG-derivations (left and right frontopolar, frontal, central and occipital electrodes, reference montage to the ipsilateral Cb) were measured (sampling rate 64(-1) s, spectral resolution.25 Hz, frequency range from.25 to 24 Hz). The interoccipital spectral coherence was generally slightly lower in the patient group; the difference was most clearly in the 12.5 to 15 Hz range of NREM sleep. www.aegis.com /aidsline/1990/apr/M9040336.html   (504 words)

 (WO/2003/081830) XDSL MULTI-HYBRID MODEM WITH POWER SPECTRAL DENSITY SHAPING   (Site not responding. Last check: 2007-11-07) Power spectral density shaping can preferably be used when the upstream transmission rate or margin has more capacity than is being used by the XDSL modem or when the downstream transmission rate is limited due to external conditions, such as bridge taps. The various spectral density processing performed by the DSP 222 may be performed using a processor and memory, and they may be controlled by software stored in the XDSL modem 200 and accessible by the DSP 222. Alternatively, the spectral density processing may be performed in hardware located in the DSP 222, or it may be performed using a combination of hardware and software. www.wipo.int /cgi-pct/guest/getbykey5?KEY=03/81830.031002&ELEMENT_SET=DECL   (8935 words)

 [No title]   (Site not responding. Last check: 2007-11-07) The spectral density of $J$ is formally defined as $\rho^J(x)={(\d \Omega_x e_0,e_0)}/{\d x}$, where $\Omega_x$ is the resolution of the identity of $J$. It is easily seen that the spectral functions of $E_t$ corresponding to the first $t$ basis vectors are given by the formula $$\rho_{(0)\,jk}(x)=\delta_{jk}{1\over 4}\rho_{\rm ch}({{x+2}\over{4}}),\qquad j,k=0,1,\dots,t-1,$$ where $\rho_{\rm ch}(\la)=\frac 8\pi\sqrt{\la(1-\la)}$ if $\la\in [0,1]$ and $\rho_{\rm ch}(\la)=0$ otherwise, is the spectral density of the J-matrix $J_{\rm ch}$ with the elements $a_i=1/2$, $b_i=1/4$, $i=0,1,\dots$. To find the spectral density of $L_t$, let us apply an arbitrary single-valued integrable function $f(x)$ to both sides of (\ref{B}) and rewrite the result in the form $$\int_{-\infty}^{\infty}f(\la)\left\{\sum_{i=0}^{t-1} \frac{\d \Omega_{\varepsilon_i}}{\d\varepsilon_i} \left\frac{\d\varepsilon_i}{\d\la}\right\right\}\d\la= \int_{-\infty}^{\infty}f(\la)\frac{\d\widetilde \Omega_{\la}} {\d\la}\d\la,\label{id}$$ where $\la=S_t(\varepsilon_i)$, $i=0,1,\dots,t-1$, and $\Omega_x$, $\widetilde \Omega_x$ are the resolutions of the identity of $L_t$ and $E_t+V$, respectively. www.ma.utexas.edu /mp_arc/html/papers/96-686   (1316 words)

 (WO/2001/011606) VOICE ACTIVITY DETECTION IN NOISY SPEECH SIGNAL   (Site not responding. Last check: 2007-11-07) Because the speech and noise signals are combined in the received signal, it is generally not possible to calculate the power spectral density of the speech signal and noise signal simultaneously. Assuming that changes in the noise signal are slow, the power spectral density of the speech signal can be calculated during the time that speech is present by subtracting the power spectral density of the noise signal (calculated when speech was not present) from the power spectral density of the received signal. This technique for calculating the power spectral density of the speech signal assumes that the speech signal and noise signal are independent, which is not always correct. www.wipo.int /cgi-pct/guest/getbykey5?KEY=01/11606.010215&ELEMENT_SET=DECL   (2438 words)

 Dirac operator spectral density and low energy sum rules The spectral density of euclidean Dirac operator is investigated in partially quenched QCD with arbitrary quark masses. A representation of scalar and pseudoscalar correlators in terms of the spectral density is discussed. The spectral density, obtained from the partially quenched chiral perturbation theory is shown to be compatible with low energy sum rules, obtained earlier. stacks.iop.org /1126-6708/2000/i=06/a=025   (264 words)

 Spectral Density In particular, an analytic continuation of the spectral density may often be made across the real axis, into a region which is not accessible by the mere solution of a differential equation. Since the spectral density is so closely related to the Weyl-Titchmarsh m function, the calculation of the latter can be used as a numerical technique for the location of the eigenvalues of a differential equation. Once the potential shows a little variability, however, it is found that the spectral density oscillates sedately, passing through a sequence of maxima and minima, whose sharpness and amplitude vary with the potential. delta.cs.cinvestav.mx /~mcintosh/comun/quant/node6.html   (1444 words)

 1 By definition, power spectral density of a stochastic process is the Fourier transform of its auto-correlation function. Another important consideration regarding to the spectral estimation is that most often the observations of the signal are corrupted by noise. In this project, we examine the estimation of the power spectral density of four stochastic processes, based on observation vectors of length 64. www.ee.umd.edu /~afshin/adsp3/report.htm   (1993 words)

 R: Spectral Density Estimation String specifying the method used to estimate the spectral density. vector of frequencies at which the spectral density is estimated. Vector (for univariate series) or matrix (for multivariate series) of estimates of the spectral density at frequencies corresponding to www.utdallas.edu /~ammann/Rabundance/Rwin/library/ts/html/spectrum.html   (287 words)

 [No title] If estimates for the spectral density function are reqested, these are computed as limits of a sequence of spectral density functions of approximating regular problems. For these regular problems the spectral density function is a step function, and is computed directly from the definition making use of computed eigenvalues and the norm reciprocals of the corresponding eigen- functions. The spectral density function displayed at the end of each iteration is the result of an h-squared extra- polation over the regular step functions generated at each level of this iteration. www.mines.edu /fs_home/spruess/sledge/sledge_doc.txt   (3421 words)

 Baseband Modulation Using Rectangular Pulses and Binary Pulse Amplitude Modulation - Tutorial - Development Library - ... As shown in Figures 3-3a–c, note that the normalized energy spectral density of a single negative rectangular pulse is the same as a single positive rectangular pulse. The normalized energy spectral densities of the four waveforms are shown in Figures 3-6a–d. As shown in Figure 3-6e, if we average the four possible normalized energy spectral densities, the result is a sinc-squared-shaped average normalized energy spectral density that corresponds to double the normalized energy spectral density of the single rectangular pulse shown in Figure 3-2. zone.ni.com /devzone/conceptd.nsf/webmain/32B8D11B01A6D6D086256E01007ECAE8   (2126 words)

 Spectral Analysis The spectral density function of a white noise is a constant. When the series is positively autocorrelated, its spectral density function is dominated by low frequencies. In practice, the population spectral density function cannot be computed. www.asu.edu /it/fyi/unix/helpdocs/statistics/sas/sasdoc/sashtml/iml/chap10/sect11.htm   (299 words)

 Power Spectral Density   (Site not responding. Last check: 2007-11-07) Power spectral density, or PSD, is a method of scaling the amplitude axis in certain spectra which consist of random rather than deterministic signals. Because a random signal has energy spread out over a frequency band, it is not meaningful to speak of its RMS value at any specific frequency. PSD is defined in terms of amplitude squared per hertz, and is thus proportional to the power delivered by the signal in a one-hertz band. www.dliengineering.com /vibman/gloss_powerspectraldensity1.htm   (91 words)

 Power Spectral Density   (Site not responding. Last check: 2007-11-07) The scalar power spectral density in a confined wake in a pipe... A power law power spectral density model of total electron content structure in... The Power Spectral Density of a Time Hopping UWB Signal: A Survey... www.scienceoxygen.com /math/599.html   (279 words)

 spectral density, periodograms, Numeric   (Site not responding. Last check: 2007-11-07) >>>>> "John" == John Hunter writes: John> Is anyone aware of cross and power spectral density John> functions for Numeric arrays using an averaged periodogram John> method. psd - Power spectral density uing Welch's average periodogram csd - Cross spectral density uing Welch's average periodogram cohere - Coherence (normalized cross spectral density) corrcoef - The matrix of correlation coefficients All functions should work for real or complex valued Numeric arrays. Coherence is the normalized cross spectral density Cxy = Pxy^2/(Pxx*Pyy) The return value is (Cxy, f), where f are the frequencies of the coherence vector. mail.python.org /pipermail/python-list/2003-January/142831.html   (362 words)

 Automatic Local Smoothing for Spectral Density Estimation - Fan, Kreutzberger (ResearchIndex)   (Site not responding. Last check: 2007-11-07) Asymptotic sampling properties of the proposed estimators are derived, and adaptation of the proposed estimator to the boundary e ect is noted. 2 Cross-validatory choice of a spectral estimate and its conne.. 2 Nonparametric spectral density estimation using penalized Wh.. citeseer.ist.psu.edu /286119.html   (658 words)

 [No title]   (Site not responding. Last check: 2007-11-07) and the spectral density of the input is Graph the spectral density of both the input and output. is observed in the presence of white noise having a spectral density of 3 V www.wmich.edu /ece/sever/BasicSkills.htm   (2987 words)

 power spectral density   (Site not responding. Last check: 2007-11-07) It is often useful to express the power spectral density in dB relative to P Since the argument of the logarithm is in units of Hz, this spectral measure can loosely be said to be in units of `dB/Hz'. shows this spectral measure in pictures of a Spectrum; it is also the units in which an Ltas and a Spectrogram are expressed. www.fon.hum.uva.nl /praat/manual/power_spectral_density.html   (190 words)

 NASA - SPECTRAL DENSITY OF LASER BEAM SCINTILLATION IN WIND TURBULENCE: I. THEORY, H-2321, April 1997, DFRC The temporal spectral density of the log-amplitude scintillation of a laser beam wave due to a spatially dependent vector-valued crosswind (deterministic as well as random) is evaluated. The path weighting functions for normalized spectral moments are derived, and offer a potential new technique for estimating the wind velocity profile. The Taylor “frozen-in” hypothesis is assumed for the dependence of the refractive index on the wind velocity, and the Kolmogorov spectral density is used for the refractive index field. www.nasa.gov /lb/centers/dryden/news/DTRS/1997/Bib/H-2321.html   (206 words)

 Power Spectral Density   (Site not responding. Last check: 2007-11-07) The power spectral density, PSD, describes how the power (or variance) of a time series is distributed with frequency. The more popular in the field of cardiovascular signals analysis are those based on the direct computation of the squared modulus of the Fourier transform of the time series (often termed periodogram estimators) through FFT, and those based on an autoregressive modeling of the time series. Power Spectral Densities obtained by Fourier transform of systolic blood pressure, SBP, (left) and RR-interval (right) time series in a young healthy subject at rest. www.cbi.dongnocchi.it /glossary/PowerSpectralDensity.html   (177 words)

 SSRN-Estimating the Rank of the Spectral Density Matrix by Gonzalo Camba-Méndez, George Kapetanios The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. The method presented is valid for any hermitian positive definite matrix estimate that has a normal asymptotic distribution with a covariance matrix the rank of which is known. Camba-Méndez, Gonzalo and Kapetanios, George, "Estimating the Rank of the Spectral Density Matrix". papers.ssrn.com /sol3/papers.cfm?abstract_id=643904   (222 words)

 R: Piecewise monotone spectral density approximation with taut strings   (Site not responding. Last check: 2007-11-07) Piecewise monotone spectral density approximation with taut strings If pks=0 then on Gaussian test beds the number of peaks of the true density is at least the returned value with an asymptotic probability of at least alpha. If mult = T then rescaled empirical density is compared with the exponential distribution only on intervals forming a multiresolution scheme. pbil.univ-lyon1.fr /library/ftnonpar/html/pmspec.html   (243 words)

 Wireless Communications: Modeling Random Fading Channels > Power Spectral Density (PSD)   (Site not responding. Last check: 2007-11-07) It turns out that the autocorrelation method and the power spectral density method in this section are related by the Wiener-Khintchine theorem, providing different perspectives of the same information. The Wiener-Khintchine theorem implies that studying autocorrelation properties in the base domain is equivalent to studying average signal power in the spectral domain. The spectral definitions for time-Doppler channels are equally valid for use with other channel dependencies. www.informit.com /articles/article.asp?p=169488&seqNum=2   (1005 words)

 Vertical unit in a power spectral density plot. - Corrosionsource.com Discussion Boards Vertical unit in a power spectral density plot. If,this noise density is constant in frequency, the integral is easy; just multiply the constant spectral power density (in v^2/Hz) by the Remember, that if you are looking at a long data trace, rms is approximately 1/5 the peak to peak noise level. www.corrosionsource.com /discuss2/ubb/Forum2/HTML/000114.html   (293 words)

 [No title]   (Site not responding. Last check: 2007-11-07) This module introduces spectral properties of random signals, such as relation of power spectral density to ACF, linear system (filter) with WSS input, and physical interpretation of power spectral density. Illustration of the different properties of wide band (upper) and narrow band (lower) random signals: (a) the signal waveforms with unit variance; (b) their autocorrelation functions (ACFs); and (c) their power spectral densities (PSDs). In (b) and (c), the thin fluctuating curves shows the actual values measured from 4000 samples of the random waveforms while the thick smooth curves show the limits of the ACF and PSD as the lengths of the waveforms tend to infinity. cnx.rice.edu /content/m11104/2.1/source   (372 words)

 Product Detail   (Site not responding. Last check: 2007-11-07) Foremost among these is the power spectral density. Principles of Random Signal Analysis and Low Noise Design presents, from a thorough signal theory basis, a comprehensive and straightforward account of the power spectral density and its applications. The author: details the power spectral density of the significant random signal forms; illustrates theory with examples from communications and electronic circuit design; presents a unified account for the power spectral density which encompasses periodic signals, aperiodic signals, and random processes, over finite and infinite intervals. shop.ieee.org /ieeestore/product.aspx?product_no=PC5934   (208 words)

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