Showing papers on "Spectral density published in 2002"

A measurement by BOOMERANG of multiple peaks in the angular power spectrum of the cosmic microwave background

Abstract: This paper presents a measurement of the angular power spectrum of the cosmic microwave background from l = 75 to l = 1025 (~10' to 24) from a combined analysis of four 150 GHz channels in the BOOMERANG experiment. The spectrum contains multiple peaks and minima, as predicted by standard adiabatic inflationary models in which the primordial plasma undergoes acoustic oscillations. These results, in concert with other types of cosmological measurements and theoretical models, significantly constrain the values of ?tot, ?bh2, ?ch2, and ns.

Degree Angular Scale Interferometer First Results: A Measurement of the Cosmic Microwave Background Angular Power Spectrum

Abstract: We present measurements of anisotropy in the cosmic microwave background (CMB) from the first season of observations with the Degree Angular Scale Interferometer (DASI). The instrument was deployed at the South Pole in the austral summer 1999-2000, and we made observations throughout the following austral winter. We present a measurement of the CMB angular power spectrum in the range 100 < l < 900 in nine bands with fractional uncertainties in the range 10%-20% and dominated by sample variance. In this paper, we review the formalism used in the analysis, in particular the use of constraint matrices to project out contaminants such as ground and point source signals and to test for correlations with diffuse foreground templates. We find no evidence of foregrounds other than point sources in the data, and we find a maximum likelihood temperature spectral index β = -0.1 ± 0.2 (1 σ), consistent with CMB. We detect a first peak in the power spectrum at l ~ 200, in agreement with previous experiments. In addition, we detect a peak in the power spectrum at l ~ 550 and power of similar magnitude at l ~ 800, which are consistent with the second and third harmonic peaks predicted by adiabatic inflationary cosmological models.

Estimating Fixed Frame Galaxy Magnitudes in the SDSS

Abstract: Broad-band measurements of flux for galaxies at different redshifts measure different regions of the rest-frame galaxy spectrum. Certain astronomical questions, such as the evolution of the luminosity function of galaxies, require transforming these magnitudes into redshift-independent quantities. To prepare to address these astronomical questions, investigated in detail in subsequent papers, we fit spectral energy distributions (SEDs) to broad band photometric observations, in the context of the optical observations of the Sloan Digital Sky Survey (SDSS). Linear combinations of four spectral templates can reproduce the five SDSS magnitudes of all galaxies to the precision of the photometry. Expressed in the appropriate coordinate system, the locus of the coefficients multiplying the templates is planar, and in fact nearly linear. The resulting reconstructed SEDs can be used to recover fixed frame magnitudes over a range of redshifts. This process yields consistent results, in the sense that within each sample the intrinsic colors of similar type galaxies are nearly constant with redshift. We compare our results to simpler interpolation methods and galaxy spectrophotometry from the SDSS. The software that generates these results is publicly available and easily adapted to handle a wide range of galaxy observations.

A parametric model for the distribution of the angle of arrival and the associated correlation function and power spectrum at the mobile station

Abstract: One of the main assumptions in Clarke's classic channel model is isotropic scattering, i.e., uniform distribution for the angle of arrival (AOA) of multipath components at the mobile station. However, in many mobile radio channels we encounter nonisotropic scattering, which strongly affects the correlation function and power spectrum of the complex envelope at the mobile receiver. We propose the use of the versatile von Mises (1918) angular distribution, which includes and/or closely approximates important distributions like uniform, impulse, cardioid, Gaussian, and wrapped Gaussian, for modeling the nonuniform AOAs at the mobile. Based on this distribution, the associated correlation function and. power spectrum of the complex envelope at the mobile receiver are derived. The utility of the new results is demonstrated by comparison with the correlation function estimates of measured data.

The Sunyaev-Zel'dovich angular power spectrum as a probe of cosmological parameters

Abstract: The angular power spectrum of the Sunyaev–Zel'dovich (SZ) effect is a powerful probe of cosmology. It is easier to detect than individual clusters in the field, is insensitive to observational selection effects and does not require a calibration between cluster mass and flux, reducing the systematic errors that dominate the cluster-counting constraints. It receives a dominant contribution from virialized cluster region between 20 and 40 per cent of the virial radius and is thus relatively insensitive to the poorly known gas physics in the cluster centre, such as cooling or (pre)heating. In this paper we derive a refined analytic prediction for the SZ angular power spectrum using the universal gas density and temperature profile and the dark matter halo mass function. The predicted power spectrum has no free parameters and fits all of the published hydrodynamic simulation results to better than a factor of 2 for 2000 < l < 10 000. We find that the angular power spectrum Cl scales as Cl∝σ78(Ωbh)2 and is almost independent of all of the other cosmological parameters. This differs from the local cluster abundance studies, which give a relation between σ8 and Ωm. We also compute the covariance matrix of Cl using the halo model and find a good agreement relative to the simulations. We argue that the best constraint from the SZ power spectrum comes from l∼ 3000, where the sampling variance is sufficiently small and the spectrum is dominated by massive clusters above 1014h−1 M⊙ for which cooling, heating and details of star formation are not very important. We estimate how well we can determine σ8(Ωbh)2/7 with sampling-variance-limited observations and find that for a several-square-degree survey with arcmin resolution one should be able to determine σ8 to within a few per cent, with the remaining uncertainty dominated by theoretical modelling. If the recent excess of the cosmic microwave background power on small scales reported by Cosmic Background Imager (CBI) and Berkeley Illinois Maryland Association (BIMA) experiments is due to the SZ effect, then we find σ8(Ωbh/0.035)0.29= 1.04 ± 0.12 at 95 per cent confidence level (statistical) and with a residual 10 per cent systematic (theoretical) uncertainty.

Measuring the broadband power spectra of active galactic nuclei with RXTE

Abstract: We have developed a Monte Carlo technique to test models for the true power spectra of intermittently sampled lightcurves against the noisy, observed power spectra, and produce a reliable estimate of the goodness of fit of the given model. We apply this technique to constrain the broadband power spectra of a sample of four Seyfert galaxies monitored by the Rossi X-ray Timing Explorer (RXTE) over three years. We show that the power spectra of three of the AGN in our sample (MCG-6-30-15, NGC5506 and NGC3516) flatten significantly towards low frequencies, while the power spectrum of NGC5548 shows no evidence of flattening. We fit two models for the flattening, a `knee' model, analogous to the low-frequency break seen in the power spectra of BHXRBs in the low state (where the power-spectral slope flattens to \alpha=0) and a `high-frequency break' model (where the power-spectral slope flattens to \alpha=1), analogous to the high-frequency break seen in the high and low-state power spectra of the classic BHXRB Cyg X-1. Both models provide good fits to the power spectra of all four AGN. For both models, the characteristic frequency for flattening is significantly higher in MCG-6-30-15 than in NGC 3516 (by factor ~10) although both sources have similar X-ray luminosities, suggesting that MCG-6-30-15 has a lower black hole mass and is accreting at a higher rate than NGC 3516. Assuming linear scaling of characteristic frequencies with black hole mass, the high accretion rate implied for MCG-6-30-15 favours the high-frequency break model for this source and further suggests that MCG-6-30-15 and possibly NGC 5506, may be analogues of Cyg X-1 in the high state [ABRIDGED].

Multiple peaks in the angular power spectrum of the cosmic microwave background: Significance and consequences for cosmology

Abstract: Three peaks and two dips have been detected in the power spectrum of the cosmic microwave background from the BOOMERANG experiment, at {ell} {approx} 210, 540, 840 and {ell} {approx} 420, 750, respectively. Using model-independent analyses, we find that all five features are statistically significant and we measure their location and amplitude. These are consistent with the adiabatic inflationary model. We also calculate the mean and variance of the peak and dip locations and amplitudes in a large 7-dimensional parameter space of such models, which gives good agreement with the model-independent estimates, and forecast where the next few peaks and dips should be found if the basic paradigm is correct. We test the robustness of our results by comparing Bayesian marginalization techniques on this space with likelihood maximization techniques applied to a second 7-dimensional cosmological parameter space, using an independent computational pipeline, and find excellent agreement: {Omega}{sub tot} = 1.02{sub -0.05}{sup +0.06} vs. 1.04 {+-} 0.05, {Omega}{sub b}h{sup 2} = 0.022{sub -0.003}{sup +0.004} vs. 0.019{sub -0.004}{sup +0.005}, and n{sub s} = 0.96{sub -0.09}{sup +0.10} vs. 0.90 {+-} 0.08. The deviation in primordial spectral index n{sub s} is a consequence of the strong correlation with the optical depth.

Spectral methods for nonstationary spatial processes

Abstract: SUMMARY We propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process. We also study the asymptotic properties of the proposed estimators via shrinking asymptotics, assuming the distance between neighbouring observations tends to zero as the size of the observation region grows without bound. With this type of asymptotic model we can uniquely determine the spectral density, avoiding the aliasing problem. We also present a new class of nonstationary processes, based on a convolution of local stationary processes. This model has the advantage that the model is simultaneously defined everywhere, unlike 'moving window' approaches, but it retains the attractive property that, locally in small regions, it behaves like a stationary spatial process. Applications include the spatial analysis and modelling of air pollution data provided by the US Environmental Protection Agency.

Generic estimate of trans-Planckian modifications to the primordial power spectrum in inflation

Abstract: We derive a general expression for the power spectra of scalar and tensor fluctuations generated during inflation given an arbitrary choice of boundary condition for the mode function at a short distance. We assume that the boundary condition is specified at a short-distance cutoff at a scale $M$ which is independent of time. Using a particular prescription for the boundary condition at momentum $p = M$, we find that the modulation to the power spectra of density and gravitational wave fluctuations is of order $(H/M)$, where $H$ is the Hubble parameter during inflation, and we argue that this behavior is generic, although by no means inevitable. With fixed boundary condition, we find that the shape of the modulation to the power spectra is determined entirely by the deviation of the background spacetime from the de Sitter limit.

Analysis of two-point statistics of cosmic shear - I. Estimators and covariances

Abstract: Recently, cosmic shear, the weak lensing effect by the inhomogeneous matter distribution in the Universe, has not only been detected by several groups, but the observational results have been used to derive constraints on cosmological parameters. For this purpose, several cosmic shear statistics have been employed. As shown recently, all second-order statistical measures can be expressed in terms of the two-point correlation functions of the shear, which thus represents the basic quantity; also, from a practical point-of-view, the two-point correlation functions are easiest to obtain from observational data which typically have complicated geometry. We derive in this paper expressions for the covariance matrix of the cosmic shear two- point correlation functions which are readily applied to any survey geometry. Furthermore, we consider the more special case of a simple survey geometry which allows us to obtain approximations for the covariance matrix in terms of integrals which are readily evaluated numerically. These results are then used to study the covariance of the aperture mass dispersion which has been employed earlier in quantitative cosmic shear analyses. We show that the aperture mass dispersion, measured at two different angular scales, quickly decorrelates with the ratio of the scales. Inverting the relation between the shear two-point correlation functions and the power spectrum of the underlying projected matter distribution, we construct estimators for the power spectrum and for the band powers, and show that they yields accurate approximations; in particular, the correlation between band powers at different wave numbers is quite weak. The covariance matrix of the shear correlation function is then used to investigate the expected accuracy of cosmological parameter estimates from cosmic shear surveys. Depending on the use of prior information, e.g. from CMB measurements, cosmic shear can yield very accurate determinations of several cosmological parameters, in particular the normalization σ8 of the power spectrum of the matter distribution, the matter density parameter Ωm, and the shape parameter Γ.

Spectral Decomposition of Two-Dimensional Atmospheric Fields on Limited-Area Domains Using the Discrete Cosine Transform (DCT)

Abstract: For most atmospheric fields, the larger part of the spatial variance is contained in the planetary scales. When examined over a limited area, these atmospheric fields exhibit an aperiodic structure, with large trends across the domain. Trying to use a standard (periodic) Fourier transform on regional domains results in the aliasing of largescale variance into shorter scales, thus destroying all usefulness of spectra at large wavenumbers. With the objective of solving this particular problem, the authors have evaluated and adopted a spectral transform called the discrete cosine transform (DCT). The DCT is a widely used transform for compression of digital images such as MPEG and JPEG, but its use for atmospheric spectral analysis has not yet received widespread attention. First, it is shown how the DCT can be employed for producing power spectra from two-dimensional atmospheric fields and how this technique compares favorably with the more conventional technique that consists of detrending the data before applying a periodic Fourier transform. Second, it is shown that the DCT can be used advantageously for extracting information at specific spatial scales by spectrally filtering the atmospheric fields. Examples of applications using data produced by a regional climate model are displayed. In particular, it is demonstrated how the 2D-DCT spectral decomposition is successfully used for calculating kinetic energy spectra and for separating mesoscale features from large scales.

On the validity of Gaussian approximation to characterize the multiuser capacity of UWB TH PPM

Abstract: Ultra-wideband time hopping binary pulse position modulation performance in a free space propagation condition is analyzed. An analytic expression for the bit error rate is obtained, in terms of signal energy-noise power spectral density ratio (E/sub x//N/sub 0/), number of users, bit rate and impulse characteristics. Multiple access interference is assumed to be a zero mean Gaussian process. Theoretical results are compared with simulation analysis and the validity of the Gaussian hypothesis is discussed.

Circumbinary disk evolution

Abstract: We study the evolution of circumbinary disks surrounding classical T Tau stars. High resolution numerical simulations are employed to model a system consisting of a central eccentric binary star within an accretion disk. The disk is assumed to be infinitesimally thin, however a detailed energy balance including viscous heating and radiative cooling is applied. A novel numerical approach using a parallelized Dual-Grid technique on two different coordinate systems has been implemented. Physical parameters of the setup are chosen to model the close system of DQ Tau and AK Sco, as well as the wider systems of GG Tau and UY Aur. Our main findings are for the tight binaries a substantial flow of material through the disk gap which is accreted onto the central stars in a phase dependent process. We are able to constrain the parameters of the systems by matching both accretion rates and derived spectral energy distributions to observational data where available.

Angle and time of arrival statistics for the Gaussian scatter density model

Abstract: Starting from a Gaussian distribution of scatterers around a mobile station, expressions are provided for the probability density function (PDF) in the angle of arrival, the power azimuth spectrum, the PDF in the time of arrival, and the time delay spectrum, all as seen from a base station. Expressions are also provided for some of the quantities of practical interest such as the root-mean-square (RMS) angular spread, the RMS delay spread, and the spatial cross-correlation function. Results for the Gaussian scatter density model are compared with those for the circular scattering model and the elliptical scattering model as well as with experimental results available for outdoor and indoor environments. Comparison is shown for the PDFs as well as for the power spectra in angle and delay. It is shown that the present model, in contrast to the previous models, produces results that closely agree with experimental results. With an appropriate choice of the standard deviation of the scattering region, the Gaussian density model can be made suitable both for environments with very small angular spreads as well as those with very large angular spreads. Consequently, the results provided in the paper are applicable to both macrocellular as well as picocellular environments.

Analysis of two-point statistics of cosmic shear: I. Estimators and covariances

Abstract: We derive in this paper expressions for the covariance matrix of the cosmic shear two-point correlation functions which are readily applied to any survey geometry. Furthermore, we consider the more special case of a simple survey geometry which allows us to obtain approximations for the covariance matrix in terms of integrals which are readily evaluated numerically. These results are then used to study the covariance of the aperture mass dispersion which has been employed earlier in quantitative cosmic shear analyses. We show that the aperture mass dispersion, measured at two different angular scales, quickly decorrelates with the ratio of the scales. Inverting the relation between the shear two-point correlation functions and the power spectrum of the underlying projected matter distribution, we construct estimators for the power spectrum and for the band powers, and show that they yields accurate approximations; in particular, the correlation between band powers at different wave numbers is quite weak. The covariance matrix of the shear correlation function is then used to investigate the expected accuracy of cosmological parameter estimates from cosmic shear surveys. Depending on the use of prior information, e.g. from CMB measurements, cosmic shear can yield very accurate determinations of several cosmological parameters, in particular the normalization $\sigma_8$ of the power spectrum of the matter distribution, the matter density parameter $\Omega_{\rm m}$, and the shape parameter $\Gamma$.

Weak Lensing Results from the 75 Square Degree CTIO Survey

Abstract: We measure seeing-corrected ellipticities for 2 x 10^6 galaxies with magnitude R 30\arcmin, ellipticity correlations are detected at high significance and exhibit nearly the pure "E-mode" behavior expected of weak gravitational lensing. Even when smoothed to the full field size of 2.5 degrees, which is ~25h^-1 Mpc at the lens distances, an rms shear variance of ^1/2 = 0.0012 +- 0.0003 is detected. At smaller angular scales there is significant "B-mode" power, an indication of residual uncorrected PSF distortions. The >30\arcmin data constrain the power spectrum of matter fluctuations on comoving scales of ~10h^-1 Mpc to have \sigma_8 (\Omega_m/0.3)^{0.57} = 0.71^{+0.12}_{-0.16} (95% CL, \LambdaCDM, \Gamma=0.21), where the systematic error includes statistical and calibration uncertainties, cosmic variance, and a conservative estimate of systematic contamination based upon the detected B-mode signal. This normalization of the power spectrum is lower than previous weak-lensing results but generally consistent them, is at the lower end of the \sigma_8 range from various analyses of galaxy cluster abundances, and agrees with recent determinations from CMB and galaxy clustering. The large and dispersed sky coverage of our survey reduces random errors and cosmic variance, while the relatively shallow depth allows us to use existing redshift-survey data to reduce systematic uncertainties in the N(z) distribution to insignificance. Reanalysis of the data with more sophisticated algorithms will hopefully reduce the systematic (B-mode) contamination, and allow more precise, multidimensional constraint of cosmological parameters.

Simulating the Sunyaev-Zel'dovich effect(s): including radiative cooling and energy injection by galactic winds

Abstract: We present results on the thermal and kinetic Sunyaev-Zel'dovich (SZ) effects from a sequence of high resolution hydrodynamic simulations of structure formation, including cooling, feedback and metal injection. These simulations represent a self-consistent thermal model which incorporates ideas from the `pre-heating' scenario while preserving good agreement with the low density IGM at z~3 probed by the Ly-a forest. Four simulations were performed, at two different resolutions with and without radiative effects and star formation. The long-wavelength modes in each simulation were the same, so that we can compare the results on an object by object basis. We demonstrate that our simulations are converged to the sub-arcminute level. The effect of the additional physics is to suppress the mean Comptonization parameter by 20% and to suppress the angular power spectrum of fluctuations by just under a factor of two in this model while leaving the source counts and properties relatively unchanged. We quantify how non-Gaussianity in the SZ maps increases the sample variance over the standard result for Gaussian fluctuations. We identify a large scatter in the Y-M relation which will be important in searches for clusters using the SZ effect(s).

Efficient cosmological parameter estimation from microwave background anisotropies

Abstract: We reexamine the issue of cosmological parameter estimation in light of current and upcoming high-precision measurements of the cosmic microwave background power spectrum. Physical quantities which determine the power spectrum are reviewed, and their connection to familiar cosmological parameters is explicated. We present a set of physical parameters, analytic functions of the usual cosmological parameters, upon which the microwave background power spectrum depends linearly (or with some other simple dependence) over a wide range of parameter values. With such a set of parameters, microwave background power spectra can be estimated with a high accuracy and negligible computational effort, vastly increasing the efficiency of the cosmological parameter error determination. The techniques presented here allow calculation of microwave background power spectra ${10}^{5}$ times faster than comparably accurate direct codes (after precomputing a handful of power spectra). We discuss various issues of parameter estimation, including parameter degeneracies, numerical precision, mapping between physical and cosmological parameters, systematic errors, and illustrate these considerations with an idealized model of the Microwave Anisotropy Probe experiment.

Matter power spectrum from the Lyman-alpha forest: myth or reality?

Abstract: We investigate possible systematic errors in the recent measurement of the matter power spectrum from the Lyman-alpha forest by Croft et al. We find that for a large set of prior cosmological models the Croft et al. result holds quite well, with systematic errors being comparable with random ones, when a dependence of the recovered-matter power spectrum on the cosmological parameters at z∼3 is taken into account. We find that peculiar velocities cause the flux power spectrum to be smoothed over about 100–300 km s-1, depending on scale. Consequently, the recovered-matter power spectrum is a smoothed version of the underlying true power spectrum. Uncertainties in the recovered power spectrum are thus correlated over about 100–300 km s-1. As a side effect, we find that residual fluctuations in the ionizing background, while having almost no effect on the recovered-matter power spectrum, significantly bias estimates of the baryon density from the Lyman-alpha forest data. We therefore conclude that the Croft et al. result provides a powerful new constraint on cosmological parameters and models of structure formation.

A unified spectral analysis of generalized time-hopping spread-spectrum signals in the presence of timing jitter

Abstract: This paper characterizes the power spectral density (PSD) of various time-hopping spread-spectrum (TH-SS) signaling schemes in the presence of random timing jitter, which is characterized typically by a discrete-time stationary random process (independent of the TH sequences and data sequence) with known statistical properties. A flexible model for a general TH-SS signal is proposed and a unified spectral analysis of this generalized TH-SS signal is carried out using a systematic and tractable technique. The key idea is to express the basic baseband pulse in terms of its Fourier transform which allows flexibility in specifying different TH formats throughout the general derivation. The power spectrum of various TH-SS signaling schemes can then be obtained as a special case of the generalized PSD results. Although general PSD results are first obtained for arbitrary timing jitter statistics, specific results are then given for the cases of practical interest, namely, uniform and Gaussian distributed jitter. Applications of this unified spectral analysis includes: (1) clocked TH by a random sequence; (2) framed TH by a random sequence; and (3) framed TH by a pseudorandom periodic sequence. Detailed descriptions of these different TH techniques are given where the first two techniques employ a random sequence (stochastic model) and the third technique employs a pseudorandom sequence (deterministic model).

Relic backgrounds of gravitational waves from cosmic turbulence

Abstract: Turbulence may have been produced in the early universe by several nonequilibrium processes. Periods of cosmic turbulence may have left a detectable relic under the form of stochastic backgrounds of gravitational waves. In this paper we derive general expressions for the power spectrum of the expected signal. Extending previous works on the subject, we take into account the effects of a continuous energy injection power and of magnetic fields. Both effects lead to relevant deviations from the Kolmogoroff turbulence spectrum. We apply our results to determine the spectrum of gravity waves which may have been produced by neutrino inhomogeneous diffusion and during a first order phase transition. We show that in both cases the expected signal may be in the sensitivity range of the interferometer LISA.

Quantum chaos and 1/f noise.

Abstract: It is shown that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum behavior of such a signal for different systems suggests the following conjecture: The energy spectra of chaotic quantum systems are characterized by 1/f noise.

Spectral analysis based on the state covariance: the maximum entropy spectrum and linear fractional parametrization

Abstract: Input spectra, which are consistent with a given state covariance of a linear filter, correspond to solutions of an analytic interpolation problem. We derive an explicit formula for the power spectrum with maximal entropy, and provide a linear fraction parametrization of all solutions.

Analysis of power and power spectral density in PWM inverters with randomized switching frequency

Abstract: A novel method for accurate calculation of power spectra of the pulsewidth modulation (PWM) voltage-source inverter with randomized switching frequency is presented. The case of a limited pool of switching frequencies, convenient and adequate for technical purposes, is considered, and a mathematical background for this type of random PWM (RPWM) is provided. It is shown that the limited-pool RPWM gives rise to not only a continuous spectrum, but, also, under certain circumstances, pure power spectral components (harmonics), typical for the deterministic PWM. Criteria for the existence of harmonics are given, and formulae for both the power and the power spectral density are derived and verified experimentally.

Envelope broadening of spherically outgoing waves in three‐dimensional random media having power law spectra

Abstract: [1] High-frequency S wave seismogram envelopes are broadened with increasing travel distance due to diffraction and scattering. The basic mechanism of the broadening has been studied on the basis of the scattering theory with the parabolic approximation for the scalar wave equation in random media. However, conventional models are not realistic enough since the plane wave modeling is too simple and the Gaussian autocorrelation function (ACF) is far from the reality to represent the inhomogeneity in the Earth. Focusing on the early part of envelopes, we formulated the envelope broadening of spherically outgoing scalar waves in three-dimensional von Karman-type random media, of which the spectra decay according to a power law at large wave numbers. Random media are characterized by three parameters: RMS fractional velocity fluctuation e, correlation distance a, and order κ that controls the gradient of the power law spectra. This model predicts that the envelope duration increases with both travel distance and frequency when short-wavelength components are rich in random media, while the duration is independent of frequency when short-wavelength components are poor. Introducing phenomenological attenuation Q, we developed a method for estimating the parameters of inhomogeneity and attenuation from the envelope duration. Applying this method to S wave seismogram envelopes for the frequency range from 2 to 32 Hz in northeastern Honshu Japan, we estimated the random inhomogeneity parameters as κ = 0.6, e2.2a−1 ≈ 10−3.6 [km−1] and f/Q = 0.0095 [s−1], where f is frequency. The power law portion of the estimated power spectral density function is P(m) ≈ 0.01 m−4.2 [km3], where m is wave number.

Frequency-dependent attenuation-compensation functions for ultrasonic signals backscattered from random media.

Abstract: Estimations of scattering parameters, such as average scatterer diameter, from rf signals backscattered from random media (tissues) are made from the frequency dependence of the rf signal. The frequency dependence of the rf signal backscattered from the medium is seen in the normalized power spectrum. The normalized power spectrum is found by taking the squared magnitude of the Fourier transform of the rf signal gated over a region of interest and dividing by some reference spectrum. If the medium has a frequency-dependent attenuation then the shape of the normalized power spectrum will be affected by the frequency-dependent attenuation and the time duration of the gated signal. Not accounting for the frequency-dependent attenuation leads to poor estimations of scatterer parameters. Larger attenuation and longer time gates give poorer estimates of scatterer parameters without attenuation compensation. Several attenuation-compensation functions have been used to account for the attenuation losses to the normalized power spectrum. A new attenuation-compensation function is proposed and compared with the other attenuation-compensation routines. The new attenuation-compensation function is shown to give improved estimates over previous attenuation-compensation functions for scatterers that follow a Gaussian form factor.

Stochastic resonance in psychophysics and in animal behavior.

Abstract: A recent analysis of the energy detector model in sensory psychophysics concluded that stochastic resonance does not occur in a measure of signal detectability ( d'), but can occur in a percent-correct measure of performance as an epiphenomenon of nonoptimal criterion placement [Tougaard (2000) Biol Cybern 83: 471-480]. When generalized to signal detection in sensory systems in general, this conclusion is a serious challenge to the idea that stochastic resonance could play a significant role in sensory processing in humans and other animals. It also seems to be inconsistent with recent demonstrations of stochastic resonance in sensory systems of both nonhuman animals and humans using measures of system performance such as signal-to-noise ratio of power spectral densities and percent-correct detections in a two-interval forced-choice paradigm, both closely related to d'. In this paper we address this apparent dilemma by discussing several models of how stochastic resonance can arise in signal detection systems, including especially those that implement a "soft threshold" at the input transform stage. One example involves redefining d' for energy increments in terms of parameters of the spike-count distribution of FitzHugh-Nagumo neurons. Another involves a Poisson spike generator that receives an exponentially transformed noisy periodic signal. In this case it can be shown that the signal-to-noise ratio of the power spectral density at the signal frequency, which exhibits stochastic resonance, is proportional to d'. Finally, a variant of d' is shown to exhibit stochastic resonance when calculated directly from the distributions of power spectral densities at the signal frequency resulting from transformation of noise alone and a noisy signal by a sufficiently steep nonlinear response function. All of these examples, and others from the literature, imply that stochastic resonance is more than an epiphenomenon, although significant limitations to the extent to which adding noise can aid detection do exist.

Minimal modifications of the primordial power spectrum from an adiabatic short distance cutoff

Abstract: As a simple model for unknown Planck scale physics, we assume that the quantum modes responsible for producing primordial curvature perturbations during inflation are placed in their instantaneous adiabatic vacuum when their proper momentum reaches a fixed high energy scale M. The resulting power spectrum is derived and presented in a form that exhibits the amplitude and frequency of the superimposed oscillations in terms of $H/M$ and the slow roll parameter $\ensuremath{\epsilon}.$ The amplitude of the oscillations is proportional to the third power of $H/M.$ We argue that these small oscillations give the lower bound of the modifications of the power spectrum if the notion of free mode propagation ceases to exist above the critical energy scale M.

Predicting spectral regrowth of nonlinear power amplifiers

Abstract: Power amplifiers (PAs) are important elements in communications systems and they are inherently nonlinear. Nonlinearity generates spectral regrowth (i.e., spectral broadening) in digitally modulated signals which causes adjacent channel interference. In this paper, we present a closed-form expression for the auto-covariance function of the PA output, whose Fourier transform yields the output power spectral density (PSD). The PA input does not need to be Gaussian and the PSD calculation can be carried out using common PA descriptions such as the AM/AM and AM/PM characteristics. We assume that the input is narrow-band, thus PA memory effects, on the order of a symbol period, are not present. The analytical results allow us to predict spectral regrowth without running expensive or time-consuming time-domain simulations; they also lead to a variety of optimization possibilities in transmitter design that includes the PAs.

The CMB power spectrum out to l=1400 measured by the VSA

Abstract: We have observed the cosmic microwave background (CMB) in three regions of sky using the Very Small Array (VSA) in an extended configuration with antennas of beamwidth 2 degrees at 34 GHz. Combined with data from previous VSA observations using a more compact array with larger beamwidth, we measure the power spectrum of the primordial CMB anisotropies between angular multipoles l = 160 - 1400. Such measurements at high l are vital for breaking degeneracies in parameter estimation from the CMB power spectrum and other cosmological data. The power spectrum clearly resolves the first three acoustic peaks, shows the expected fall off in power at high l and starts to constrain the position and height of a fourth peak.