Techniques and errors in measuring cross- correlation and cross-spectral density functions
Instrument errors and data reduction techniques for dynamic pressure cross correlation and cross spectral density function measurements
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Instrument errors and data reduction techniques for dynamic pressure cross correlation and cross spectral density function measurements
Techniques and errors in measuring cross spectral density and cross correlation functions of stationary dynamic pressure data
The cross-correlation functions (CCFs) and cross spectra expected for quasi-periodic oscillation (QPO) shot noise models are calculated under various assumptions, and the results are compared to observations. Effects due to possible coherence of the QPO oscillations are included. General formulas for the cross spectrum, the cross-phase spectrum, and the time-delay spectrum for QPO shot models are calculated and discussed. It is shown that the CCFs, cross spectra, and power spectra observed for Cyg X-e2 imply that the spectrum of the shots evolves with time, with important implications for the interpretation of these functions as well as of observed average energy spectra. The possible origins for the observed hard lags are discussed, and some physical difficulties for the Comptonization model are described. Classes of physical models for QPO sources are briefly addressed, and it is concluded that models involving shot formation at the surface of neutron stars are favored by observation.
Cross-correlations of galaxy positions and galaxy shears with maps of gravitational lensing of the cosmic microwave background (CMB) are sensitive to the distribution of large-scale structure in the Universe. Such cross-correlations are also expected to be immune to some of the systematic effects that complicate correlation measurements internal to galaxy surveys. We present measurements and modeling of the cross-correlations between galaxy positions and galaxy lensing measured in the first three years of data from the Dark Energy Survey with CMB lensing maps derived from a combination of data from the 2500 deg 2 SPT-SZ survey conducted with the South Pole Telescope and full-sky data from the Planck satellite. The CMB lensing maps used in this analysis have been constructed in a way that minimizes biases from the thermal Sunyaev Zel’dovich effect, making them well suited for cross-correlation studies. The total signal-to-noise of the cross-correlation measurements is 23.9 (25.7) when using a choice of angular scales optimized for a linear (nonlinear) galaxy bias model. Here we use the cross-correlation measurements to obtain constraints on cosmological parameters. For our fiducial galaxy sample, which consist of four bins of magnitude-selected galaxies, we find constraints of Ω m =0.272$^{+0.032}_{-0.052}$ and S 8 ≡σ8$\sqrt{Ω_m/0.3}$=0.736$^{+0.032}_{-0.028}$ (Ω m =0.245$^{+0.026}_{-0.044}$ and S 8 =0.734$^{+0.035}_{-0.028}$) when assuming linear (nonlinear) galaxy bias in our modeling. Considering only the cross-correlation of galaxy shear with CMB lensing, we find Ω m =0.270$^{+0.043}_{-0.061}$ and S 8 =0.740$^{+0.034}_{-0.029}$. Our constraints on S8 are consistent with recent cosmic shear measurements, but lower than the values preferred by primary CMB measurements from Planck.
Here we present a tomographic measurement of the cross-correlation between thermal Sunyaev-Zel’dovich (TSZ) maps from Planck and the Atacama Cosmology Telescope and weak galaxy lensing shears measured during the first three years of observations of the Dark Energy Survey. This correlation is sensitive to the thermal energy in baryons over a wide redshift range and is therefore a powerful probe of astrophysical feedback. We detect the correlation at a statistical significance of 21σ, the highest significance to date. We examine the TSZ maps for potential contaminants, including cosmic infrared background and radio sources, finding that cosmic infrared background has a substantial impact on our measurements and must be taken into account in our analysis. We use the cross-correlation measurements to test different feedback models. In particular, we model the TSZ using several different pressure profile models calibrated against hydrodynamical simulations. Our analysis marginalizes over redshift uncertainties, shear calibration biases, and intrinsic alignment effects. We also marginalize over Ω m and σ 8 using Planck or DES priors. We find that the data prefer the model with a low amplitude of the pressure profile at small scales, compatible with a scenario with strong active galactic nuclei feedback and ejection of gas from the inner part of the halos. When using a more flexible model for the shear profile, constraints are weaker, and the data cannot discriminate between different baryonic prescriptions.
Digital cross correlator design for impulse response determination in linear systems, noting real time operation without software and storage problems
Cross correlation function plots were used to determine if peak distortion data taken from a subscale inlet model can be used to predict peak distortion levels for a full scale flight test vehicle.
Hot, ionized gas leaves an imprint on the cosmic microwave background via the thermal Sunyaev-Zel’dovich (tSZ) effect. The cross-correlation of gravitational lensing (which traces the projected mass) with the tSZ effect (which traces the projected gas pressure) is a powerful probe of the thermal state of ionized baryons throughout the Universe and is sensitive to effects such as baryonic feedback. In a companion paper (Gatti et al. Phys. Rev. D 105, 123525 (2022)), we present tomographic measurements and validation tests of the cross-correlation between Galaxy shear measurements from the first three years of observations of the Dark Energy Survey and tSZ measurements from a combination of Atacama Cosmology Telescope and Planck observations. In this work, we use the same measurements to constrain models for the pressure profiles of halos across a wide range of halo mass and redshift. We find evidence for reduced pressure in low-mass halos, consistent with predictions for the effects of feedback from active Galactic nuclei. We infer the hydrostatic mass bias (B ≡ M 500c /M SZ from our measurements, finding B = 1.8 ± 0.1 when adopting the Planck-preferred cosmological parameters. We additionally find that our measurements are consistent with a nonzero redshift evolution of B, with the correct sign and sufficient magnitude to explain the mass bias necessary to reconcile cluster count measurements with the Planck-preferred cosmology. Our analysis introduces a model for the impact of intrinsic alignments (IAs) of galaxy shapes on the shear-tSZ correlation. We show that IA can have a significant impact on these correlations at current noise levels.
Waveform cross-correlation is a sensitive phase-matched filtering technique that can detect seismic events for nuclear explosion monitoring. However, there are outstanding challenges with correlation detectors, most notably a direct dependence on the completeness of the waveform template library. To ameliorate these challenges, we investigate how dynamic time warping (DTW) may make waveform correlation more robust. DTW analyzes the differences between two time series and attempts to “warp” one time series relative to another in a recursive manner. We apply DTW to synthetic earthquake and recorded explosion templates to expand the capability of correlation detectors. We explore what conditions (e.g., source, station distance, frequency bands) and/or DTW algorithms generate stronger correlation scores. We show that DTW performs well on noisy signals and can dramatically improve the cross-correlation coefficient between a template and data-stream waveform. We conclude with recommendations on how to utilize DTW in nuclear monitoring detection.
Cross-correlation techniques are used to measure the sound radiated by wing/flap airfoil configurations in the NASA-Ames 40 x 80 ft wind tunnel using a 6.7-m semispan model with three deployed flaps. The dominant source of flap noise is identified as the flap side edges, which exceeds that radiated by the midspan region by more than 10 dB. The turbulent surface eddies at the flap side edge have scales on the order of one-half the flap chord. The installation of flap actuator fairings at the flap side edge reduces the noise radiated from that location by 10 to 15 dB. The cross-correlation technique extracts airframe noise radiated by specific surface locations from the tunnel background noise, even when the noise is 25 dB higher than the measured airframe noise level.
Cross relation and cross spectral methods of computing drift velocity of structure undergoing internal rearrangement for remote solar wind observation
Optical cross correlation method for remote sensing applications
Stabilized cross correlation radiometer for use at decametric wavelength, using two feedback loops controlling four noise diodes
ABSTRACT Cross-correlations between data sets are used in many different contexts in cosmological analyses. Recently, k-nearest neighbour cumulative distribution functions (kNN-CDF) were shown to be sensitive probes of cosmological (auto) clustering. In this paper, we extend the framework of NN measurements to describe joint distributions of, and correlations between, two data sets. We describe the measurement of joint kNN-CDFs, and show that these measurements are sensitive to all possible connected N-point functions that can be defined in terms of the two data sets. We describe how the cross-correlations can be isolated by combining measurements of the joint kNN-CDFs and those measured from individual data sets. We demonstrate the application of these measurements in the context of Gaussian density fields, as well as for fully non-linear cosmological data sets. Using a Fisher analysis, we show that measurements of the halo-matter cross-correlations, as measured through NN measurements are more sensitive to the underlying cosmological parameters, compared to traditional two-point cross-correlation measurements over the same range of scales. Finally, we demonstrate how the NN cross-correlations can robustly detect cross-correlations between sparse samples – the same regime where the two-point cross-correlation measurements are dominated by noise.
According to one embodiment, a cross-correlator comprises a plurality of analog front ends (AFEs), a cross-correlation circuit and a data serializer. Each of the AFEs comprises a variable gain amplifier (VGA) and a corresponding analog-to-digital converter (ADC) in which the VGA receives and modifies a unique analog signal associates with a measured analog radio frequency (RF) signal and the ADC produces digital data associated with the modified analog signal. Communicatively coupled to the AFEs, the cross-correlation circuit performs a cross-correlation operation on the digital data produced from different measured analog RF signals. The data serializer is communicatively coupled to the summing and cross-correlating matrix and continuously outputs a prescribed amount of the correlated digital data.
We study the cross-correlation of damped Lyα systems (DLAs) and their background quasars, using the most updated DLA catalog and the Planck 2018 CMB lensing convergence field. Our measurement suggests that the DLA bias b DLA is smaller than 3.1, corresponding to log (M/M ⊙ h -1 ) ⩽ 12.3 at a confidence of 90%. These constraints are broadly consistent with Alonso et al. and previous measurements by cross-correlation between DLAs and the Lyα forest (e.g., Font-Ribera et al.; Prez-Rfols et al.). Further, our results demonstrate the potential of obtaining a more precise measurement of the halo mass of the high-redshift sources using next generation CMB experiments with a higher angular resolution. The python-based codes and data products of our analysis are available at https://github.com/LittleLin1999/CMB-lensingxDLA.
The use of cross-correlation for certain types of spectral analysis is discussed. Under certain circumstances, the use of cross-correlation between a real spectrum and either a model or another spectrum can provide a very powerful tool for spectral analysis. The method (and its limitations) will be described with concrete examples using ATMOS data.
Computer implemented phase-slope and cross-correlation methods are introduced for measuring time delays between pairs of broadband ultrasonic pulse-echo signals for determining velocity in engineering materials. The phase-slope and cross-correlation methods are compared with the overlap method which is currently in wide use. Comparison of digital versions of the three methods shows similar results for most materials having low ultrasonic attenuation. However, the cross-correlation method is preferred for highly attenuating materials. An analytical basis for the cross-correlation method is presented. Examples are given for the three methods investigated to measure velocity in representative materials in the megahertz range.