Journal articles: 'Power Specturm'

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Fedi, Maurizio, Tatiana Quarta, and Angelo De Santis. "Inherent power‐law behavior of magnetic field power spectra from a Spector and Grant ensemble." GEOPHYSICS 62, no. 4 (July 1997): 1143–50. http://dx.doi.org/10.1190/1.1444215.

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The Spector and Grant method, which has been in use for 25 years, relates average depths to source to rate of decay of the magnetic power spectra. This method, which assumes a uniform distribution of parameters for an ensemble of magnetized blocks, leads to a depth‐dependent exponential rate of decay. We show that also inherent in this model is a power‐law rate of decay that is independent of depth. For most cases, except for extreme depths and small block sizes, the observed power spectrum should be corrected for a power law decay rate of β∼3. If the depth distribution of the magnetic blocks is Gaussian, then the observed power spectrum should be corrected for both a depth independent power law and exponential decay. This power‐law decay is very similar to the scaling behavior, supposed as a fractal character, of observed magnetic fields in North America. As a general rule, when β∼3, further information is needed to discriminate between a fractal or Spector and Grant model. However, it is becoming quite clear that magnetic power spectra should be corrected for a power law decay before applying the Spector and Grant method for depth determination.

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Deepali, Deepali, and Supratik Banerjee. "Scale-dependent anisotropy of electric field fluctuations in solar wind turbulence." Monthly Notices of the Royal Astronomical Society: Letters 504, no. 1 (March 17, 2021): L1—L6. http://dx.doi.org/10.1093/mnrasl/slab027.

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ABSTRACT We study the variation of average powers and spectral indices of electric field fluctuations with respect to the angle between average flow direction and the mean magnetic field in solar wind turbulence. Cluster spacecraft data from the years 2002 and 2007 are used for the present analysis. We perform a scale-dependent study with respect to the local mean magnetic field using wavelet analysis technique. Prominent anisotropies are found for both the spectral index and power levels of the electric power spectra. Similar to the magnetic field fluctuations, the parallel (or antiparallel) electric fluctuation spectrum is found to be steeper than the perpendicular spectrum. However, the parallel (or antiparallel) electric power is found to be greater than the perpendicular one. Below 0.1 Hz, the slope of the parallel electric power spectra deviates substantially from that of the total magnetic power spectra, supporting the existence of Alfvénic turbulence.

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Koch, Eric W., I.-Da Chiang (江宜達), Dyas Utomo, Jérémy Chastenet, Adam K. Leroy, Erik W. Rosolowsky, and Karin M. Sandstrom. "Spatial power spectra of dust across the Local Group: No constraint on disc scale height." Monthly Notices of the Royal Astronomical Society 492, no. 2 (December 20, 2019): 2663–82. http://dx.doi.org/10.1093/mnras/stz3582.

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ABSTRACT We analyse the 1D spatial power spectra of dust surface density and mid to far-infrared emission at $24\!-\!500\, \mu$m in the LMC, SMC, M31, and M33. By forward-modelling the point spread function (PSF) on the power spectrum, we find that nearly all power spectra have a single power-law and point source component. A broken power-law model is only favoured for the LMC 24 μm MIPS power spectrum and is due to intense dust heating in 30 Doradus. We also test for local power spectrum variations by splitting the LMC and SMC maps into 820 pc boxes. We find significant variations in the power-law index with no strong evidence for breaks. The lack of a ubiquitous break suggests that the spatial power spectrum does not constrain the disc scale height. This contradicts claims of a break where the turbulent motion changes from 3D to 2D. The power spectrum indices in the LMC, SMC, and M31 are similar (2.0–2.5). M33 has a flatter power spectrum (1.3), similar to more distant spiral galaxies with a centrally-concentrated H2 distribution. We compare the power spectra of H i, CO, and dust in M31 and M33, and find that H i power spectra are consistently flatter than CO power spectra. These results cast doubt on the idea that the spatial power spectrum traces large scale turbulent motion in nearby galaxies. Instead, we find that the spatial power spectrum is influenced by (1) the PSF on scales below ∼3 times the FWHM, (2) bright compact regions (30 Doradus), and (3) the global morphology of the tracer (an exponential CO disc).

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Jang, Doyoung, Jongmann Kim, Yong Bae Park, and Hosung Choo. "Study of an Atmospheric Refractivity Estimation from a Clutter Using Genetic Algorithm." Applied Sciences 12, no. 17 (August 26, 2022): 8566. http://dx.doi.org/10.3390/app12178566.

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In this paper, a method for estimating atmospheric refractivity from sea and land clutters is proposed. To estimate the atmospheric refractivity, clutter power spectrums based on an artificial tri-linear model are calculated using an Advanced Refractive Prediction System (AREPS) simulator. Then, the clutter power spectrums are again obtained based on the measured atmospheric refractivity data using the AREPS simulator. In actual operation, this spectrum from measured reflectivity can be replaced with real-time clutter spectrums collected from radars. A cost function for the genetic algorithm (GA) is then defined based on the difference between the two clutter power spectrums to predict the atmospheric refractivity using the artificial tri-linear model. The optimum variables of the tri-linear model are determined at a minimum cost in the GA process. The results demonstrate that atmospheric refractivity can be predicted using the proposed method from the clutter powers.

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Unruh, J. F., and D. D. Kana. "Power/Response Spectrum Transformations in Equipment Qualification." Journal of Pressure Vessel Technology 107, no. 2 (May 1, 1985): 197–202. http://dx.doi.org/10.1115/1.3264434.

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Since its introduction a few years ago the use of the power/response spectrum transformation has gained considerable interest and acceptance, and a number of new applications of the transformation have been developed in the equipment qualification area. A brief review of the power/response spectrum transformation is given with a discussion of the input/output relationships for linear systems required for elevated power spectrum generation. Frequency content of earthquakelike signals is discussed with emphasis on the resolution given by the PSD. The problem of excessive ZPA due to inconsistent spectra enveloping and mechanical nonlinearities is also discussed. The PSD/RS transformation is applied to the problems of combining various dynamic load events, developing bounding spectra, and developing damping consistent test spectra. Development of elevated component spectra corrected for base overtest and generation from in-situ measurements is reviewed.

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Kurita, Toshiki, Masahiro Takada, Takahiro Nishimichi, Ryuichi Takahashi, Ken Osato, and Yosuke Kobayashi. "Power spectrum of halo intrinsic alignments in simulations." Monthly Notices of the Royal Astronomical Society 501, no. 1 (November 25, 2020): 833–52. http://dx.doi.org/10.1093/mnras/staa3625.

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ABSTRACT We use a suite of N-body simulations to study intrinsic alignments (IA) of halo shapes with the surrounding large-scale structure in the ΛCDM model. For this purpose, we develop a novel method to measure multipole moments of the three-dimensional power spectrum of the E-mode field of halo shapes with the matter/halo distribution, $P_{\delta E}^{(\ell)}(k)$ (or $P^{(\ell)}_{{\rm h}E}$), and those of the auto-power spectrum of the E-mode, $P^{(\ell)}_{EE}(k)$, based on the E/B-mode decomposition. The IA power spectra have non-vanishing amplitudes over the linear to non-linear scales, and the large-scale amplitudes at k ≲ 0.1 h−1 Mpc are related to the matter power spectrum via a constant coefficient (AIA), similar to the linear bias parameter of galaxy or halo density field. We find that the cross- and auto-power spectra PδE and PEE at non-linear scales, k ≳ 0.1 h−1 Mpc, show different k-dependences relative to the matter power spectrum, suggesting a violation of the non-linear alignment model commonly used to model contaminations of cosmic shear signals. The IA power spectra exhibit baryon acoustic oscillations, and vary with halo samples of different masses, redshifts, and cosmological parameters (Ωm, S8). The cumulative signal-to-noise ratio for the IA power spectra is about 60 per cent of that for the halo density power spectrum, where the super-sample covariance is found to give a significant contribution to the total covariance. Thus our results demonstrate that the IA power spectra of galaxy shapes, measured from imaging and spectroscopic surveys for an overlapping area of the sky, can be used to probe the underlying matter power spectrum, the primordial curvature perturbations, and cosmological parameters, in addition to the standard galaxy density power spectrum.

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Czarnecki, Mirosław A. "Two-Dimensional Correlation Spectroscopy: The Power of Power Spectra." Applied Spectroscopy 74, no. 8 (June 8, 2020): 894–99. http://dx.doi.org/10.1177/0003702820931156.

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Power spectra are a powerful tool provided by two-dimensional correlation analysis. However, this tool is seldom used in practice. This work shows selected examples of using of the power spectra for the study of various kinds of samples with the aim to promote more common use of this tool. By examination of the power spectrum of specific sample, one can estimate the sensitivity of different molecular fragments on a given perturbation. Determination of the power spectra for smaller data subsets provides information on the dynamics of perturbation-induced spectral changes. If the experimental spectra of different samples in the same perturbation window are recorded, the comparison of the power spectra yields information on differences in the sensitivity of various samples on common perturbation. This possibility is particularly useful for studies of the spectra-structure correlations, interactions, and molecular dynamics. A comparison of the power spectra obtained by using different reference spectra provides information on the nature of spectral changes at different wavenumbers.

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Jackson, Ross A. "Haunted Across the Political Spectrum: The Specter of Communism in Two Midcentury American Organizations." International Journal of Languages, Literature and Linguistics 7, no. 4 (December 2021): 149–56. http://dx.doi.org/10.18178/ijlll.2021.7.4.303.

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Organizations operating in midcentury America experienced a period of relative economic prosperity and global power. While political tensions existed between the United States and the Soviet Union since the culmination of the World War II, when the Soviet Union conducted its first nuclear test in 1949 and then successfully launched Sputnik 1 in 1957, these political tensions became more pressing concerns to American organizations. In fact, the perceived existential threat posed by communism became an observable rhetorical justification for organization and action within the United States. Through the use of corpus linguistics techniques, a comparative analysis was conducted on the foundational documents of the rightwing, John Birch Society and the leftwing, Students for a Democratic Society. Relative word frequencies, collocations, concordancing and statistical analyses were conducted around the use and context of the keyword communism. The results suggest that while these radical and reactionary groups perceived a common threat, multifinality exists in terms of organizational response. This insight is useful to those engaged in strategy development and rhetoric for political and business organizations.

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Cheng, Yun-Ting, and Tzu-Ching Chang. "Cosmic Near-infrared Background Tomography with SPHEREx Using Galaxy Cross-correlations." Astrophysical Journal 925, no. 2 (February 1, 2022): 136. http://dx.doi.org/10.3847/1538-4357/ac3aee.

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Abstract The extragalactic background light (EBL) consists of integrated light from all sources of emission throughout the history of the universe. At near-infrared wavelengths, the EBL is dominated by stellar emission across cosmic time; however, the spectral and redshift information of the emitting sources is entangled and cannot be directly measured by absolute photometry or fluctuation measurements. Cross-correlating near-infrared maps with tracers of known redshift enables EBL redshift tomography, as EBL emission will only correlate with external tracers from the same redshift. Here, we forecast the sensitivity of probing the EBL spectral energy distribution as a function of redshift by cross-correlating the upcoming near-infrared spectro-imaging survey, SPHEREx, with several current and future galaxy redshift surveys. Using a model galaxy luminosity function, we estimate the cross power spectrum clustering amplitude on large scales, and forecast that the near-infrared EBL spectrum can be detected tomographically out to z ∼ 6. We also predict a high-significance measurement (∼102–104 σ) of the small-scale cross power spectrum out to z ∼ 10. The amplitudes of the large-scale cross power spectra can constrain the cosmic evolution of the stellar synthesis process through both continuum and the line emission, while on the nonlinear and Poisson noise scales, the high-sensitivity measurements can probe the mean spectra associated with the tracer population across redshift.

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Karaçaylı, Naim Göksel, Andreu Font-Ribera, and Nikhil Padmanabhan. "Optimal 1D Ly α forest power spectrum estimation – I. DESI-lite spectra." Monthly Notices of the Royal Astronomical Society 497, no. 4 (August 14, 2020): 4742–52. http://dx.doi.org/10.1093/mnras/staa2331.

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ABSTRACT The 1D Ly α forest flux power spectrum P1D is sensitive to scales smaller than a typical galaxy survey, and hence ties to the intergalactic medium’s thermal state, suppression from neutrino masses, and new dark matter models. It has emerged as a competitive framework to study new physics, but also has come with various challenges and systematic errors in analysis. In this work, we revisit the optimal quadratic estimator for P1D, which is robust against the relevant problems such as pixel masking, time evolution within spectrum, and quasar continuum errors. We further improve the estimator by introducing a fiducial power spectrum, which enables us to extract more information by alleviating the discreteness of band powers. We meticulously apply our method to synthetic Dark Energy Spectroscopic Instrument (DESI) spectra and demonstrate how the estimator overcomes each challenge. We further apply an optimization scheme that approximates the Fisher matrix to three elements per row and reduces computation time by 60 per cent. We show that we can achieve per cent precision in P1D with 5-yr DESI data in the absence of systematics and provide forecasts for different spectral qualities.

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Shi, Feng, Yong-Seon Song, Jacobo Asorey, David Parkinson, Kyungjin Ahn, Jian Yao, Le Zhang, and Shifan Zuo. "HIR4: cosmological signatures imprinted on the cross-correlation between a 21-cm map and galaxy clustering." Monthly Notices of the Royal Astronomical Society 499, no. 4 (November 4, 2020): 4613–25. http://dx.doi.org/10.1093/mnras/staa2914.

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ABSTRACT We explore the cosmological multitracer synergies between an emission-line galaxy distribution from the Dark Energy Spectroscopic Instrument and a Tianlai Project 21-cm intensity map. We use simulated maps generated from a particle simulation in the light-cone volume (Horizon Run 4), sky-trimmed and including the effects of foreground contamination, its removal and instrument noise. We first validate how the foreground residual affects the recovered 21-cm signal by putting different levels of foreground contamination into the 21-cm maps. We find that the contamination cannot be ignored in the angular autocorrelation power spectra of H i even when it is small, but it has no influence on the accuracy of the angular cross-correlation power spectra between H i and galaxies. In the foreground-cleaned map case, as information is lost in the cleaning procedure, there is also a bias in the cross-correlation power spectrum. However, we found that the bias from the cross-correlation power spectrum is scale-independent, which is easily parametrized as part of the model, while the offset in the H i autocorrelation power spectrum is non-linear. In particular, we tested that the cross-correlation power also benefits from the cancellation of the bias in the power spectrum measurement that is induced by the instrument noise, which changes the shape of the autocorrelation power spectra but leaves the cross-correlation power spectra unaffected. We then modelled the angular cross-correlation power spectra to fit the baryon acoustic oscillation feature in the broad-band shape of the angular cross-correlation power spectrum, including contamination from the residual foreground and the effect of instrument noise. We forecast a constraint on the angular diameter distance DA for the Tianlai Pathfinder redshift 0.775 < z < 1.03, giving a distance measurement with a precision of 2.7 per cent at that redshift.

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Riazati Seresht, Hamed, Seyed Mohammad Ahadi, and Sanaz Seyedin. "Spectro-temporal Power Spectrum Features for Noise Robust ASR." Circuits, Systems, and Signal Processing 36, no. 8 (November 22, 2016): 3222–42. http://dx.doi.org/10.1007/s00034-016-0434-0.

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Kim, Dong Sik, and Eunae Lee. "Noise Power Spectrum of Radiography Detectors: I. Measurement Using the Averages of Images." Journal of the Institute of Electronics and Information Engineers 53, no. 12 (December 25, 2016): 120–27. http://dx.doi.org/10.5573/ieie.2016.53.12.120.

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Lee, Meena, Soonmu Kwon, and Kwon Su Chon. "Analysis of Noise Power Spectrum According to Flat-Field Correction in Digital Radiography." Journal of the Korean Society of Radiology 7, no. 3 (June 30, 2013): 227–32. http://dx.doi.org/10.7742/jksr.2013.7.3.227.

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Abramenko, Valentina, and Olga Kutsenko. "Magnetic power spectrum in the undisturbed solar photosphere." Acta Astrophysica Taurica 1, no. 1 (April 13, 2020): 1–5. http://dx.doi.org/10.31059/aat.vol1.iss1.pp1-5.

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Using the magnetic field data obtained with the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO), an investigation of magnetic power spectra in the undisturbed solar photosphere was performed. The results are as follows. 1) To get a reliable estimate of a magnetic power spectrum from the uniformly distributed quiet-sun magnetic flux, a sample pattern of no less than 300 pixels length should be adopted. With smaller patterns, energy on all observable scales might be overestimated. 2) For patterns of different magnetic intensity (e.g., a coronal hole, a quiet-sun area, an area of supergranulation), the magnetic power spectra in a range of (2.5-10) Mm exhibit very close spectral indices of about -1. The observed spectrum is more shallow than the Kolmogorov-type spectrum (with a slope of -5/3) and it differs from steep spectra of active regions. Such a shallow spectrum cannot be explained by the only direct Kolmogorov’s cascade, but it can imply a small-scale turbulent dynamo action in a wide range of scales: from tens of megameters down to at least 2.5 Mm. On smaller scales, the HMI/SDO data do not allow us to reliably derive the shape of the spectrum. 3) Data make it possible to conclude that a uniform mechanism of the small-scale turbulent dynamo is at work all over the solar surface outside active regions.

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Neyrinck, Mark C. "REJUVENATING THE MATTER POWER SPECTRUM. III. THE COSMOLOGY SENSITIVITY OF GAUSSIANIZED POWER SPECTRA." Astrophysical Journal 742, no. 2 (November 9, 2011): 91. http://dx.doi.org/10.1088/0004-637x/742/2/91.

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Blake, Chris. "Power spectrum modelling of galaxy and radio intensity maps including observational effects." Monthly Notices of the Royal Astronomical Society 489, no. 1 (August 5, 2019): 153–67. http://dx.doi.org/10.1093/mnras/stz2145.

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ABSTRACT Fluctuations in the large-scale structure of the Universe contain significant information about cosmological physics, but are modulated in survey data sets by various observational effects. Building on existing literature, we provide a general treatment of how fluctuation power spectra are modified by a position-dependent selection function, noise, weighting, smoothing, pixelization, and discretization. Our work has relevance for the spatial power spectrum analysis of galaxy surveys with spectroscopic or accurate photometric redshifts, and radio intensity-mapping surveys of the sky brightness temperature including generic noise, telescope beams, and pixelization. We consider the autopower spectrum of a field, the cross-power spectrum between two fields and the multipoles of these power spectra with respect to a curved sky, deriving the corresponding power spectrum models, estimators, errors, and optimal weights. We note that ‘FKP weights’ for individual tracers do not in general provide the optimal weights when measuring the cross-power spectrum. We validate our models using mock data sets drawn fromN-body simulations.1 Our treatment should be useful for modelling and studying cosmological fluctuation fields in observed and simulated data sets.

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Yeom, Hong-Gi, Cheol-Hun Han, Ho-Duck Kim, and Kwee-Bo Sim. "Human Emotion Recognition using Power Spectrum of EEG Signals : Application of Bayesian Networks and Relative Power Values." Journal of Korean Institute of Intelligent Systems 18, no. 2 (April 25, 2008): 251–56. http://dx.doi.org/10.5391/jkiis.2008.18.2.251.

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Chen, Huiguo, Yingmin Li, and Junru Ren. "Fully Nonstationary Spatially Variable Ground Motion Simulations Based on a Time-Varying Power Spectrum Model." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/293182.

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By analyzing the evolutionary spectrum method for multivariate nonstationary stochastic processes, a simulation method for fully nonstationary spatially variable ground motion is proposed based on the Kameda time-varying power spectrum model. This method can properly simulate nonstationary spatially variable ground motion based on a target response spectrum. Two numerical examples, in which the Kameda time-varying power spectra are calculated for different conditions, are presented to demonstrate the capabilities of the proposed method. In the first example, the nonstationary spatially variable ground motion that satisfies the time-frequency characteristics and response characteristics of the original ground motion is simulated by identifying the parameters of the given time-varying power spectrum. In the second example, the ground motion that satisfies the design response spectra is simulated by defining the parameters of the time-varying power spectrum directly. The results demonstrate that the method can effectively simulate nonstationary spatially variable ground motion, which implies that the proposed method can be used in engineering applications.

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Brown, Timothy M. "Automated p-mode identification using Bayes' theorem." Symposium - International Astronomical Union 123 (1988): 491–94. http://dx.doi.org/10.1017/s0074180900158590.

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The task of interpreting p-mode spectra is complicated by the presence of a very large number of oscillation modes, each of which may appear (because of aliasing) in the power spectra corresponding to several values of l and m. Identifying peaks in a power spectrum with particular modes in an interactive fashion thus quickly becomes impractical. Here I describe an automated method for doing this identification. The method is based on an application of Bayes' theorem, which provides a simple way to use prior knowledge about the oscillation spectrum. The method takes as input the observed power spectra, and a model of the amplitudes and frequencies one expects to see.

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Kito, Shuichiro, Koosuke Hattori, Ryo Taguchi, and Taizo Umezaki. "The Feature Extraction Method in Power Spectrum Images for Connector Parts." Journal of the Institute of Industrial Applications Engineers 3, no. 4 (October 25, 2015): 154–60. http://dx.doi.org/10.12792/jiiae.3.154.

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Christian, John T. "Generating Seismic Design Power Spectral Density Functions." Earthquake Spectra 5, no. 2 (May 1989): 351–68. http://dx.doi.org/10.1193/1.1585526.

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The most widely used way to describe earthquake motions for purposes of design is the response spectrum, but it is often difficult to apply a response spectrum when dealing with multiple degrees of freedom or with complex representations of structural behavior. The power spectral density function, which is a more fundamental description of the frequency content of ground motion, has found increasing use and is essential in the most popular methods of developing artificial earthquake time histories. Although in theory the response spectrum and the power spectral density are closely related, in practice it has proven difficult to compute one from the other. Two integration schemes described in the literature have been implemented in an interactive micro-computer program SPEED and are found to give substantially identical results. When they are used to find a power spectral density function that corresponds to a standard design response spectrum, the results do not converge at frequencies above 10 Hz. Possible explanations for this lie in the shape of the prescribed standard response spectra, the methodology used to generate them, and the lack of statistical variation at high frequencies. When power spectral density functions are calculated for response spectra determined from a statistical evaluation of strong motion across the full range of frequencies, the calculations converge rapidly.

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Pal, Srikanta, Pallav Chanda, and Rajib Saha. "Estimation of the Full-sky Power Spectrum between Intermediate and Large Angular Scales from Partial-sky CMB Anisotropies Using an Artificial Neural Network." Astrophysical Journal 945, no. 1 (March 1, 2023): 77. http://dx.doi.org/10.3847/1538-4357/acb4ee.

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Abstract Reliable extraction of cosmological information from observed cosmic microwave background (CMB) maps may require removal of strongly foreground-contaminated regions from the analysis. In this paper, we employ an artificial neural network (ANN) to predict the full-sky CMB angular power spectrum between intermediate and large angular scales from the partial-sky spectrum obtained from a masked CMB temperature anisotropy map. We use a simple ANN architecture with one hidden layer containing 895 neurons. Using 1.2 × 105 training samples of full-sky and corresponding partial-sky CMB angular power spectra at HEALPix pixel resolution parameter N side = 256, we show that the spectrum predicted by our ANN agrees well with the target spectrum at each realization for the multipole range 2 ≤ l ≤ 512. The predicted spectra are statistically unbiased, and they preserve the cosmic variance accurately. Statistically, the differences between the mean predicted and underlying theoretical spectra are within approximately 3σ. Moreover, the probability densities obtained from predicted angular power spectra agree very well with those obtained from “actual” full-sky CMB angular power spectra for each multipole. Interestingly, our work shows that the significant correlations in input cut-sky spectra due to mode–mode coupling introduced on the partial sky are effectively removed, since the ANN learns the hidden pattern between the partial- and full-sky spectra preserving all of the statistical properties. The excellent agreement of statistical properties between the predicted and the ground truth demonstrates the importance of using artificial intelligence systems in cosmological analysis more widely.

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Brémaud, Pierre, Laurent Massoulié, and Andrea Ridolfi. "Power spectra of random spike fields and related processes." Advances in Applied Probability 37, no. 4 (December 2005): 1116–46. http://dx.doi.org/10.1239/aap/1134587756.

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In this article, we review known results and present new ones concerning the power spectra of large classes of signals and random fields driven by an underlying point process, such as spatial shot noises (with random impulse response and arbitrary basic stationary point processes described by their Bartlett spectra) and signals or fields sampled at random times or points (where the sampling point process is again quite general). We also obtain the Bartlett spectrum for the general linear Hawkes spatial branching point process (with random fertility rate and general immigrant process described by its Bartlett spectrum). We then obtain the Bochner spectra of general spatial linear birth and death processes. Finally, we address the issues of random sampling and linear reconstruction of a signal from its random samples, reviewing and extending former results.

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Brémaud, Pierre, Laurent Massoulié, and Andrea Ridolfi. "Power spectra of random spike fields and related processes." Advances in Applied Probability 37, no. 04 (December 2005): 1116–46. http://dx.doi.org/10.1017/s0001867800000690.

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In this article, we review known results and present new ones concerning the power spectra of large classes of signals and random fields driven by an underlying point process, such as spatial shot noises (with random impulse response and arbitrary basic stationary point processes described by their Bartlett spectra) and signals or fields sampled at random times or points (where the sampling point process is again quite general). We also obtain the Bartlett spectrum for the general linear Hawkes spatial branching point process (with random fertility rate and general immigrant process described by its Bartlett spectrum). We then obtain the Bochner spectra of general spatial linear birth and death processes. Finally, we address the issues of random sampling and linear reconstruction of a signal from its random samples, reviewing and extending former results.

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Wiedemann, K. E., J. Unnam, and R. K. Clark. "Computer Program for Deconvoluting Powder Diffraction Spectra." Powder Diffraction 2, no. 3 (September 1987): 137–45. http://dx.doi.org/10.1017/s0885715600012628.

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AbstractA program is presented that removes broadening from X-ray diffraction spectra. An instrumental spectrum can be used to describe empirically the broadening to be removed, or a Gaussian, Cauchy, or Pearson-VII distribution can be used to analytically describe it. In either case, singlet or doublet forms can be generated. The program returns the deconvoluted spectrum, the reconstructed spectrum, and a sum-of-squares difference between the original and reconstructed spectra. Deconvolution is accomplished using a combination of least-squares, background, and smoothing criteria that minimizes the effect of random counting errors.

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Persson, P. B., H. Stauss, O. Chung, U. Wittmann, and T. Unger. "Spectrum analysis of sympathetic nerve activity and blood pressure in conscious rats." American Journal of Physiology-Heart and Circulatory Physiology 263, no. 5 (November 1, 1992): H1348—H1355. http://dx.doi.org/10.1152/ajpheart.1992.263.5.h1348.

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This study tests whether the power spectrum of blood pressure (BP) provides information toward the sympathovagal balance of BP control by comparing the BP (femoral arterial catheter) spectrum with the spectrum of the efferent sympathetic nerve activity (SNA, bipolar electrode around splanchnic nerve). A remarkable resemblance between both spectra was found. A high-frequency component (HF) linked to respiration and a slower fluctuation type between 0.15 and 0.6 Hz (LF) were identified. There was a large and significant coherence only in the HF range of the BP and SNA power spectrum (P < 0.01). The phase lag of SNA and BP was roughly 200 ms. The recordings were repeated during pharmacological blockade in nine Wistar-Kyoto rats (WKY) and nine spontaneously hypertensive rats (SHR). alpha 1-Adrenoceptor blockade (prazosin) reduced the proportional LF power of BP in both rat strains (WKY P < 0.01, SHR P < 0.05) in favor of HF (WKY P < 0.01, SHR P < 0.01). Parasympathetic blockade (methylscopolamine) had no effect on proportions of power. Similarly, there were no significant differences in the proportional HF and LF power spectra of WKY and SHR. These data provide direct evidence for a relationship between the BP and SNA power spectra; however, only the acute changes in the sympathetic tone changed the LF-HF relationship.

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Grosjean, Mathieu, Marc-Antoine Dupret, Kevin Belkacem, Josefina Montalbán, and Reza Samadi. "Energy of solar-like oscillations in red giants." Proceedings of the International Astronomical Union 9, S301 (August 2013): 341–44. http://dx.doi.org/10.1017/s1743921313014555.

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AbstractCoRoT and Kepler observations of red giants reveal a large variety of spectra of nonradial solar-like oscillations. So far, we understood pretty well the link between the global properties of the star (radius, mass, evolutionary state) and the properties of the oscillation spectrum (Δν, νmax, period spacing). We are interested here in the theoretical predictions of two other components of a power spectrum, the mode linewidths and heights. The study of the energy of the oscillations is of great importance to predict the peak parameters in the power spectrum. We will discuss circumstances under which mixed modes are detectable for red-giant stellar models from 1 to 2 M⊙, with emphasis on the effect of the evolutionary status of the star along the red-giant branch on theoretical power spectra.

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Lanciani, A., S. Mariani, M. Casaioli, C. Accadia, and N. Tartaglione. "A multiscale approach for precipitation verification applied to the FORALPS case studies." Advances in Geosciences 16 (April 9, 2008): 3–9. http://dx.doi.org/10.5194/adgeo-16-3-2008.

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Abstract. Multiscale methods, such as the power spectrum, are suitable diagnostic tools for studying the second order statistics of a gridded field. For instance, in the case of Numerical Weather Prediction models, a drop in the power spectrum for a given scale indicates the inability of the model to reproduce the variance of the phenomenon below the correspondent spatial scale. Hence, these statistics provide an insight into the real resolution of a gridded field and must be accurately known for interpolation and downscaling purposes. In this work, belonging to the EU INTERREG IIIB Alpine Space FORALPS project, the power spectra of the precipitation fields for two intense rain events, which occurred over the north-eastern alpine region, have been studied in detail. A drop in the power spectrum at the shortest scales (about 30 km) has been found, as well as a strong matching between the precipitation spectrum and the spectrum of the orography. Furthermore, it has also been shown how the spectra help understand the behavior of the skill scores traditionally used in Quantitative Precipitation Forecast verification, as these are sensitive to the amount of small scale detail present in the fields.

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Treumann, Rudolf A., Wolfgang Baumjohann, and Yasuhito Narita. "On the ion-inertial-range density-power spectra in solar wind turbulence." Annales Geophysicae 37, no. 2 (April 3, 2019): 183–99. http://dx.doi.org/10.5194/angeo-37-183-2019.

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Abstract. A model-independent first-principle first-order investigation of the shape of turbulent density-power spectra in the ion-inertial range of the solar wind at 1 AU is presented. Demagnetised ions in the ion-inertial range of quasi-neutral plasmas respond to Kolmogorov (K) or Iroshnikov–Kraichnan (IK) inertial-range velocity–turbulence power spectra via the spectrum of the velocity–turbulence-related random-mean-square induction–electric field. Maintenance of electrical quasi-neutrality by the ions causes deformations in the power spectral density of the turbulent density fluctuations. Assuming inertial-range K (IK) spectra in solar wind velocity turbulence and referring to observations of density-power spectra suggest that the occasionally observed scale-limited bumps in the density-power spectrum may be traced back to the electric ion response. Magnetic power spectra react passively to the density spectrum by warranting pressure balance. This approach still neglects contribution of Hall currents and is restricted to the ion-inertial-range scale. While both density and magnetic turbulence spectra in the affected range of ion-inertial scales deviate from K or IK power law shapes, the velocity turbulence preserves its inertial-range shape in the process to which spectral advection turns out to be secondary but may become observable under special external conditions. One such case observed by WIND is analysed. We discuss various aspects of this effect, including the affected wave-number scale range, dependence on the angle between mean flow velocity and wave numbers, and, for a radially expanding solar wind flow, assuming adiabatic expansion at fast solar wind speeds and a Parker dependence of the solar wind magnetic field on radius, also the presumable limitations on the radial location of the turbulent source region.

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Cai, Jian-hua. "Fault diagnosis of rolling bearing based on empirical mode decomposition and higher order statistics." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 9 (July 28, 2014): 1630–38. http://dx.doi.org/10.1177/0954406214545820.

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In order to solve the problem of the faulted rolling bearing signal getting easily affected by Gaussian noise, a new fault diagnosis method was proposed based on empirical mode decomposition and high-order statistics. Firstly, the vibration signal was decomposed by empirical mode decomposition and the correlation coefficient of each intrinsic mode function was calculated. These intrinsic mode function components, which have a big correlation coefficient, were selected to estimate its higher order spectrum. Then based on the higher order statistics theory, this method uses higher order spectrum of each intrinsic mode function to reconstruct its power spectrum. And these power spectrums were summed to obtain the primary power spectrum of bearing signal. Finally, fault feature information was extracted from the reconstructed power spectrum. A model, using higher order spectrum to reconstruct power spectrum, was established. Meanwhile, analysis was conducted by using the simulated data and the recorded vibration signals which include inner race, out race, and bearing ball fault signal. Results show that the presented method is superior to traditional power spectrum method in suppressing Gaussian noise and its resolution is higher. New method can extract more useful information compared to the traditional method.

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32

Edwards, Timothy S. "Power Delivered to Mechanical Systems by Random Vibrations." Shock and Vibration 16, no. 3 (2009): 261–71. http://dx.doi.org/10.1155/2009/457216.

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This paper develops deformational response power descriptions of multiple degree-of-freedom systems due to stationary random vibration excitation. Two new concepts are developed. The deformational response power density (DRPD) can be computed when a structure's natural frequencies and modal masses are available. The DRPD shows the spectral content of the deformational power delivered to a specific structure by the stationary, random excitation. This function can be found through a weighted windowing of the power spectrum of the input acceleration excitation. Deformational response input power spectra (DRIPS), similar to the input energy spectrum and shock response spectrum, give the power delivered to single-degree-of-freedom systems as a function of natural frequency. It is shown that the DRIPS is simply a smoothed version of the power spectrum of the input acceleration excitation. The DRIPS gives rise to a useful power-based data smoothing operation.

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Day, Aaron, David Tytler, and Bharat Kambalur. "Power spectrum of the flux in the Lyman-alpha forest from high-resolution spectra of 87 QSOs." Monthly Notices of the Royal Astronomical Society 489, no. 2 (August 12, 2019): 2536–54. http://dx.doi.org/10.1093/mnras/stz2214.

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Abstract We measure and calibrate the power spectrum of the flux in the Ly α forest at 1.8 < z < 4.6 for wavenumbers 0.003 ≤ k ≤ 0.1 s km−1 from the spectra of 87 QSOs obtained with HIRES on the Keck-I telescope. This is the largest sample using high-resolution spectra, yielding the smallest statistical errors, and we have applied calibrations to reduce new systematic errors. We fit Voigt profiles to the damped Ly α absorbers and we remove them. We subtract metal lines statistically based on metal absorption on the red side of the Ly α emission peak. We find that when performing a statistical subtraction of metal lines, a systematic offset due to the blending of metal and hydrogen lines must be taken into account. This offset was not accounted for in previous analyses, and requires up to a $3 {{\ \rm per\ cent}}$ reduction in the BOSS Ly α forest flux power spectrum, increasing the allowed neutrino mass. For the first time in a Ly α forest power spectrum measurement from high-resolution spectra, we correct for spectral leakage by applying Welch’s window function. Our treatment of metal line removal as well as our elimination of errors due to spectral leakage leads to a more accurate measurement of the Ly α forest power spectrum at the smallest scales. We find evidence that previously published values of the power are systematically too high at scales log k ≥ −1.3 (k ≥ 0.05) s km−1, which implies that the intergalactic medium is hotter than previously deduced from the Ly α forest flux power spectrum.

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Pelgrims, V., E. Ntormousi, and K. Tassis. "The effect of cosmic variance on the characteristics of dust polarization power spectra." Astronomy & Astrophysics 658 (February 2022): A134. http://dx.doi.org/10.1051/0004-6361/202141879.

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In the context of cosmic microwave background polarization studies and the characterization of the Galactic foregrounds, the power spectrum analysis of the thermal dust polarization sky has led to intriguing evidence of an E∕B asymmetry and a positive TE correlation. In this work, we produce synthesized dust polarization maps from a set of global magneto-hydrodynamic (MHD) simulations of Milky-Way-sized galaxies, and analyze their power spectra at intermediate angular scales (intermediate angular multipoles ℓ∈[60, 140]). We study the role of the initial configuration of the large-scale magnetic field, its strength, and the feedback on the power spectrum characteristics. Using full-galaxy MHD simulations, we were able to estimate the variance induced by the peculiar location of the observer in the galaxy. We find that the polarization power spectra sensitively depend on the observer’s location, impeding a distinction between different simulation setups. In particular, there is a clear statistical difference between the power spectra measured from within the spiral arms and those measured from the inter-arm regions. Also, power spectra from within supernova-driven bubbles share common characteristics, regardless of the underlying model. However, no correlation was found between the statistical properties of the polarization power spectra and the local (with respect to the observer) mean values of physical quantities such as the density and the strength of the magnetic field. Finally, we find some indications that the global strength of the magnetic field may play a role in shaping the power spectrum characteristics; as the global magnetic field strength increases, the E∕B asymmetry and the TE correlation increase, whereas the viewpoint-induced variance decreases. However, we find no direct correlation with the strength of the local magnetic field that permeates the mapped region of the interstellar medium.

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Chang, Zhe, Xukun Zhang, and Jing-Zhi Zhou. "The cosmological vector modes from a monochromatic primordial power spectrum." Journal of Cosmology and Astroparticle Physics 2022, no. 10 (October 1, 2022): 084. http://dx.doi.org/10.1088/1475-7516/2022/10/084.

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Abstract The cosmological background of higher order vector modes can be generated by the first order scalar perturbations. We investigate the second order and the third order vector modes in a radiation-dominated era systematically. The explicit expressions of two point functions 〈V (n),λ V (n),λ' 〉(n = 2,3) and corresponding power spectra are presented. In the case of a monochromatic primordial power spectrum, the second order vector modes do not exist. However, the third order vector modes can be generated by a monochromatic primordial power spectrum. And it is found that the third order vector modes sourced by the second order scalar perturbations dominate the two point function 〈V (3),λ V (3),λ' 〉 and corresponding power spectra.

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Parker, M. L., W. N. Alston, Z. Igo, and A. C. Fabian. "Modelling X-ray RMS spectra I: intrinsically variable AGNs." Monthly Notices of the Royal Astronomical Society 492, no. 1 (December 10, 2019): 1363–69. http://dx.doi.org/10.1093/mnras/stz3470.

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ABSTRACT We present simple xspec models for fitting excess variance spectra of active galactic nuclei. Using a simple Monte Carlo approach, we simulate a range of spectra corresponding to physical parameters varying, then calculate the resulting variance spectra. Starting from a variable power law, we build up a set of models corresponding to the different physical processes that can affect the final excess variance spectrum. We show that the complex excess variance spectrum of IRAS 13224−3809 can be well described by such an intrinsic variability model, where the power-law variability is damped by relativistic reflection and enhanced by an ultra-fast outflow. The reflection flux is correlated with that of the power law, but not perfectly. We argue that this correlation is stronger at high frequencies, where reverberation lags are detected, while excess variance spectra are typically dominated by low-frequency variability.

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Divine, D. V., and F. Godtliebsen. "Bayesian modeling and significant features exploration in wavelet power spectra." Nonlinear Processes in Geophysics 14, no. 1 (February 12, 2007): 79–88. http://dx.doi.org/10.5194/npg-14-79-2007.

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Abstract. This study proposes and justifies a Bayesian approach to modeling wavelet coefficients and finding statistically significant features in wavelet power spectra. The approach utilizes ideas elaborated in scale-space smoothing methods and wavelet data analysis. We treat each scale of the discrete wavelet decomposition as a sequence of independent random variables and then apply Bayes' rule for constructing the posterior distribution of the smoothed wavelet coefficients. Samples drawn from the posterior are subsequently used for finding the estimate of the true wavelet spectrum at each scale. The method offers two different significance testing procedures for wavelet spectra. A traditional approach assesses the statistical significance against a red noise background. The second procedure tests for homoscedasticity of the wavelet power assessing whether the spectrum derivative significantly differs from zero at each particular point of the spectrum. Case studies with simulated data and climatic time-series prove the method to be a potentially useful tool in data analysis.

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Pan, Yulin, Brian K. Arbic, Arin D. Nelson, Dimitris Menemenlis, W. R. Peltier, Wentao Xu, and Ye Li. "Numerical Investigation of Mechanisms Underlying Oceanic Internal Gravity Wave Power-Law Spectra." Journal of Physical Oceanography 50, no. 9 (September 1, 2020): 2713–33. http://dx.doi.org/10.1175/jpo-d-20-0039.1.

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AbstractWe consider the power-law spectra of internal gravity waves in a rotating and stratified ocean. Field measurements have shown considerable variability of spectral slopes compared to the high-wavenumber, high-frequency portion of the Garrett–Munk (GM) spectrum. Theoretical explanations have been developed through wave turbulence theory (WTT), where different power-law solutions of the kinetic equation can be found depending on the mechanisms underlying the nonlinear interactions. Mathematically, these are reflected by the convergence properties of the so-called collision integral (CL) at low- and high-frequency limits. In this work, we study the mechanisms in the formation of the power-law spectra of internal gravity waves, utilizing numerical data from the high-resolution modeling of internal waves (HRMIW) in a region northwest of Hawaii. The model captures the power-law spectra in broad ranges of space and time scales, with scalings ω−2.05±0.2 in frequency and m−2.58±0.4 in vertical wavenumber. The latter clearly deviates from the GM76 spectrum but is closer to a family of induced-diffusion-dominated solutions predicted by WTT. Our analysis of nonlinear interactions is performed directly on these model outputs, which is fundamentally different from previous work assuming a GM76 spectrum. By applying a bicoherence analysis and evaluations of modal energy transfer, we show that the CL is dominated by nonlocal interactions between modes in the power-law range and low-frequency inertial motions. We further identify induced diffusion and the near-resonances at its spectral vicinity as dominating the formation of power-law spectrum.

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Molina, R. A., J. Retamosa, L. Muñoz, A. Relaño, and E. Faleiro. "Power spectrum of nuclear spectra with missing levels and mixed symmetries." Physics Letters B 644, no. 1 (January 2007): 25–32. http://dx.doi.org/10.1016/j.physletb.2006.10.058.

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Xu, Long Jun, and Hong Zhi Zhang. "The Uncertainty in Shape Parameter Predictions of Seismic Design Spectra for Nuclear Power Plant." Applied Mechanics and Materials 405-408 (September 2013): 2025–29. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.2025.

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Aiming at the uncertainty of design spectrum raised by the construction methods, a comparative study is conducted in which different methodologies performed calculations of seismic response spectra using the same set of ground motion data from recent large earthquakes. The results of the research allowed some estimates to be made of the scaling method and model uncertainty involved in these calculations. These results were compared with the uncertainty derived from the proposed spectrum of a double-parameter-based bi-normalized response spectrum (DPBNS) approach. It is concluded that the sources of uncertainty that the results reflected are mainly impacted by the spectral type, scaling parameters, as well as imposed fixed conditions adopted in the calculations, for the scaling of the design spectra. Then, a discussion is provided on the limitations of these predications, in particular, of the approaches adopted in the construction of seismic spectra.

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Gao, Jing, Rihan Wu, and Jinde Zhang. "An Adaptive Multi-Target Jamming Waveform Design Based on Power Minimization." Entropy 22, no. 5 (April 29, 2020): 508. http://dx.doi.org/10.3390/e22050508.

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With increasing complexity of electronic warfare environments, smart jammers are beginning to play an important role. This study investigates a method of power minimization-based jamming waveform design in the presence of multiple targets, in which the performance of a radar system can be degraded according to the jammers’ different tasks. By establishing an optimization model, the power consumption of the designed jamming spectrum is minimized. The jamming spectrum with power control is constrained by a specified signal-to-interference-plus-noise ratio (SINR) or mutual information (MI) requirement. Considering that precise characterizations of the radar-transmitted spectrum are rare in practice, a single-robust jamming waveform design method is proposed. Furthermore, recognizing that the ground jammer is not integrated with the target, a double-robust jamming waveform design method is studied. Simulation results show that power minimization-based single-robust jamming spectra can maximize the power-saving performance of smart jammers in the local worst-case scenario. Moreover, double-robust jamming spectra can minimize the power consumption in the global worst-case scenario and provide useful guidance for the waveform design of ground jammers.

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Choudhury, Madhurima, Abhirup Datta, and Suman Majumdar. "Extracting the 21-cm power spectrum and the reionization parameters from mock data sets using artificial neural networks." Monthly Notices of the Royal Astronomical Society 512, no. 4 (March 17, 2022): 5010–22. http://dx.doi.org/10.1093/mnras/stac736.

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ABSTRACT Detection of the H i 21-cm power spectrum is one of the key science drivers of several ongoing and upcoming low-frequency radio interferometers. However, the major challenge in such observations come from bright foregrounds, whose accurate removal or avoidance is key to the success of these experiments. In this work, we demonstrate the use of artificial neural networks (ANNs) to extract the H i 21-cm power spectrum from synthetic data sets and extract the reionization parameters from the H i 21-cm power spectrum. For the first time, using a suite of simulations, we present an ANN-based framework capable of extracting the H i signal power spectrum directly from the total observed sky power spectrum (which contains the 21-cm signal, along with the foregrounds and effects of the instrument). We have used a combination of two ANNs sequentially. In the first step, ANN1 predicts the 21-cm power spectrum directly from foreground corrupted synthetic data sets. In the second step, ANN2 predicts the reionization parameters from the predicted H i power spectra from ANN1. The two-step ANN framework can be used as an alternative method to extract the 21-cm power spectrum and the reionization parameters directly from foreground dominated data sets. Our ANN-based framework is trained at a redshift of 9.01, and for $\boldsymbol {k}$ modes in the range, $\rm {0.17\lt {\boldsymbol {k}}\lt 0.37~Mpc^{-1}}$. We have tested the network’s performance with mock data sets corrupted with thermal noise corresponding to 1080 h of observations of the SKA-1 LOW and HERA. We have recovered the H i power spectra from foreground dominated synthetic data sets, with an accuracy of $\approx 95{\!-\!}99{{\ \rm per\ cent}}$. We have achieved an accuracy of $\approx ~81{\!-\!}90{{\ \rm per\ cent}}$ and $\approx ~50{\!-\!}60{{\ \rm per\ cent}}$ for the predicted reionization parameters, for test sets corrupted with thermal noise corresponding to the SKA-1 LOW and HERA, respectively.

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Lakshmi, V. Anantha, Satheesh G, and T. Bramhananda Reddy. "Power Spectral Density Estimation and THD of Motor Line Currents of AZSPWM Based DTC of Induction Motor Drive." International Journal of Engineering & Technology 7, no. 4.24 (November 27, 2018): 42. http://dx.doi.org/10.14419/ijet.v7i4.24.21853.

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Estimating the power distribution over a given frequency range and the total harmonic distortion of the line currents of the AZSPWM based induction motor drive is discussed in this paper. Applying a spectrum analysis on the motor line currents and inspecting the spectrum amplitudes at different switching frequencies for abnormality is a well-known procedure for acoustic noise detection and diagnosis. Among the spectrum analysis techniques for acoustic noise detection, the Fast Fourier Transform (FFT) is the most widely used technique. There are other spectrum techniques, which are based on the power spectral density (PSD) estimates. AZSPWM based DTC of induction motor currents are estimated for the power spectral densities. The harmonic spectra and the power spectral density estimates of all AZSPWM family are validated through the MATLAB/ simulink environment.

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Ran Tao, Feng Zhang, and Yue Wang. "Fractional Power Spectrum." IEEE Transactions on Signal Processing 56, no. 9 (September 2008): 4199–206. http://dx.doi.org/10.1109/tsp.2008.925579.

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Asahara, Masaki. "Noise Power Spectrum." Japanese Journal of Radiological Technology 65, no. 12 (2009): 1671–79. http://dx.doi.org/10.6009/jjrt.65.1671.

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Patil, S. P., N. R. Phadnis, and S. A. Patil. "Power Spectrum Analysis." IETE Technical Review 17, no. 3 (May 2000): 119–21. http://dx.doi.org/10.1080/02564602.2000.11416892.

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Porqueres, Natalia, Alan Heavens, Daniel Mortlock, and Guilhem Lavaux. "Bayesian forward modelling of cosmic shear data." Monthly Notices of the Royal Astronomical Society 502, no. 2 (January 25, 2021): 3035–44. http://dx.doi.org/10.1093/mnras/stab204.

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ABSTRACT We present a Bayesian hierarchical modelling approach to infer the cosmic matter density field, and the lensing and the matter power spectra, from cosmic shear data. This method uses a physical model of cosmic structure formation to infer physically plausible cosmic structures, which accounts for the non-Gaussian features of the gravitationally evolved matter distribution and light-cone effects. We test and validate our framework with realistic simulated shear data, demonstrating that the method recovers the unbiased matter distribution and the correct lensing and matter power spectrum. While the cosmology is fixed in this test, and the method employs a prior power spectrum, we demonstrate that the lensing results are sensitive to the true power spectrum when this differs from the prior. In this case, the density field samples are generated with a power spectrum that deviates from the prior, and the method recovers the true lensing power spectrum. The method also recovers the matter power spectrum across the sky, but as currently implemented, it cannot determine the radial power since isotropy is not imposed. In summary, our method provides physically plausible inference of the dark matter distribution from cosmic shear data, allowing us to extract information beyond the two-point statistics and exploiting the full information content of the cosmological fields.

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Chandra, Rajorshi Sushovan, and Tarun Souradeep. "Primordial Power Spectrum reconstruction from CMB Weak Lensing Power Spectrum." Journal of Cosmology and Astroparticle Physics 2021, no. 10 (October 1, 2021): 081. http://dx.doi.org/10.1088/1475-7516/2021/10/081.

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Abstract We use the modified and improved Richardson-Lucy (IRL) deconvolution algorithm to reconstruct the Primordial Power Spectrum (PPS) from the Weak Lensing Power Spectrum CL ϕϕ reconstructed from CMB anisotropies. This provides an independent window to observe and constrain the PPS PR (k) along different k scales as compared to CMB Temperature Power Spectrum. The Weak Lensing Power Spectrum does not contain secondary variations in power and hence is cleaner, unlike the Temperature Power Spectrum which suffers from lensing which must be addressed during PPS reconstructions. We demonstrate that the physical behaviour of the weak lensing kernel is unique and reconstructs broad features over k. We provide an in-depth analysis of the error propagation using simulated data and Monte-Carlo sampling, using Planck best-fit cosmological parameters to simulate the data with cosmic variance limited error bars. The error and initial condition analyses provide a clear picture of the optimal reconstruction region for the estimator while providing a detailed statistical insight of the results. We also provide an algorithm for PR (k) sampling sparsity to be used based on the given data and errors, to optimize statistical significance. Eventually we plan to use this method on actual mission data and provide a cross reference to PPS reconstructed from other sectors and any possible features in them.

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Kim, J. D., Jin Seok Oh, Myung Hyun Lee, and Y. S. Kim. "Spectroscopic Analysis of Plasma Induced in Laser Welding of Aluminum Alloys." Materials Science Forum 449-452 (March 2004): 429–32. http://dx.doi.org/10.4028/www.scientific.net/msf.449-452.429.

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This paper describes the features and characteristics of plasma induced in the pulsed YAG laser welding of Al-Mg alloys in air and argon atmospheres. In the air environment, the identified spectra are atomic lines of Al, Mg, Cr, Mn, Fe and Zn, and singly ionized Mg line, as well as strong molecular spectrum of AlO, MgO and AlH. It has been confirmed that the resonant lines of Al and Mg were strongly self-absorbed. These facts have shown that the laser-induced plasma is relatively a low temperature and high density metallic vapor. The intensities of molecular spectra of AlO and MgO are different each other depending on the power density of laser beam. Under the low power density irradiation condition, the MgO band spectrum is predominant in intensity, while the AlO spectrum became much stronger with the increase in high power density. This was attributed by the great difference in boiling point and vaporization energy of Al and Mg. In argon atmosphere the band spectra of MgO and AlO completely vanished, but AlH molecular spectra is detected clearly. The hydrogen source is presumably the hydrogen solved in the base metal, absorbed water on the surface oxide layer, or H2 and H2O in the shielding gas.

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Philcox, Oliver H. E., and Daniel J. Eisenstein. "Computing the small-scale galaxy power spectrum and bispectrum in configuration space." Monthly Notices of the Royal Astronomical Society 492, no. 1 (November 28, 2019): 1214–42. http://dx.doi.org/10.1093/mnras/stz3335.

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ABSTRACT We present a new class of estimators for computing small-scale power spectra and bispectra in configuration space via weighted pair and triple counts, with no explicit use of Fourier transforms. Particle counts are truncated at $R_0\sim 100\, h^{-1}\, \mathrm{Mpc}$ via a continuous window function, which has negligible effect on the measured power spectrum multipoles at small scales. This gives a power spectrum algorithm with complexity $\mathcal {O}(NnR_0^3)$ (or $\mathcal {O}(Nn^2R_0^6)$ for the bispectrum), measuring N galaxies with number density n. Our estimators are corrected for the survey geometry and have neither self-count contributions nor discretization artefacts, making them ideal for high-k analysis. Unlike conventional Fourier-transform-based approaches, our algorithm becomes more efficient on small scales (since a smaller R0 may be used), thus we may efficiently estimate spectra across k-space by coupling this method with standard techniques. We demonstrate the utility of the publicly available power spectrum algorithm by applying it to BOSS DR12 simulations to compute the high-k power spectrum and its covariance. In addition, we derive a theoretical rescaled-Gaussian covariance matrix, which incorporates the survey geometry and is found to be in good agreement with that from mocks. Computing configuration- and Fourier-space statistics in the same manner allows us to consider joint analyses, which can place stronger bounds on cosmological parameters; to this end we also discuss the cross-covariance between the two-point correlation function and the small-scale power spectrum.

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Journal articles on the topic 'Power Specturm'

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