THE COVARIANCE OF EXTERNAL SHOT NOISE AT A SENSOR ARRAY

Geophysics ◽  
1973 ◽  
Vol 38 (5) ◽  
pp. 957-958
Author(s):  
T. S. Edrington
Keyword(s):  
Power Spectrum ◽  
Bessel Function ◽  
Shot Noise ◽  
Sensor Array ◽  
Random Noise ◽  
Zero Order ◽  
Random Combination ◽  
Order Bessel Function ◽  
Single Sensor ◽  
Cross Power Spectrum

Noise (of seismic and other origins) is often modeled as a shot process, i.e., as a random combination of wavelets. Specifically, if X is the random noise process and g is the deterministic waveform of the wavelet, then [Formula: see text]where the [Formula: see text] are Poisson points in time. One useful result (derived by Backus et al., 1964) under this model is that if the wavelets are propagating across a sensor array, and if the wavelet origins are uniformly distributed in azimuth, then the cross‐power spectrum for a pair of sensors is the product of the power spectrum at a single sensor and a zero‐order Bessel function. In the notation of Backus et al., [Formula: see text]

scholarly journals Elements of harmonic analysis related to the third basic zero order Bessel function

2008 ◽  
Vol 342 (2) ◽  
pp. 1203-1219 ◽  
Author(s):  
Néji Bettaibi ◽  
Fethi Bouzeffour ◽  
Hédi Ben Elmonser ◽  
Wafa Binous
Keyword(s):  
Harmonic Analysis ◽  
Bessel Function ◽  
Zero Order ◽  
The Third ◽  
Order Bessel Function

Improved Triangular Window Apodization Function Based on Zero-Order Bessel Function

2020 ◽  
Vol 40 (3) ◽  
pp. 0307001
Author(s):  
邓竞蓝 Deng Jinglan ◽  
童晶晶 Tong Jingjing ◽  
高闽光 Gao Minguang ◽  
李相贤 Li Xiangxian ◽  
李妍 Li Yan ◽  
...  
Keyword(s):  
Bessel Function ◽  
Zero Order ◽  
Order Bessel Function ◽  
Apodization Function

scholarly journals Interpretation of MUSIC for Location Detecting of Small Inhomogeneities Surrounded by Random Scatterers

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Won-Kwang Park
Keyword(s):  
Bessel Function ◽  
Zero Order ◽  
Signal Classification ◽  
Music Algorithm ◽  
Multiple Signal Classification ◽  
Multiple Signal ◽  
Order Bessel Function

We consider the MUltiple SIgnal Classification (MUSIC) algorithm for identifying the locations of small electromagnetic inhomogeneities surrounded by random scatterers. For this purpose, we rigorously analyze the structure of MUSIC-type imaging function by establishing a relationship with zero-order Bessel function of the first kind. This relationship shows certain properties of the MUSIC algorithm, explains some unexplained phenomena, and provides a method for improvements.

scholarly journals The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: a multitracer analysis in Fourier space for measuring the cosmic structure growth and expansion rate

2021 ◽  
Vol 504 (1) ◽  
pp. 33-52
Author(s):  
Gong-Bo Zhao ◽  
Yuting Wang ◽  
Atsushi Taruya ◽  
Weibing Zhang ◽  
Héctor Gil-Marín ◽  
...  
Keyword(s):  
Growth Rate ◽  
Power Spectrum ◽  
Confidence Level ◽  
Expansion Rate ◽  
Fourier Space ◽  
Redshift Range ◽  
Significance Level ◽  
Data Product ◽  
New Development ◽  
Cross Power Spectrum

ABSTRACT We perform a joint BAO and RSD analysis using the eBOSS DR16 LRG and ELG samples in the redshift range of z ∈ [0.6, 1.1], and detect an RSD signal from the cross-power spectrum at a ∼4σ confidence level, i.e., fσ8 = 0.317 ± 0.080 at zeff = 0.77. Based on the chained power spectrum, which is a new development in this work to mitigate the angular systematics, we measure the BAO distances and growth rate simultaneously at two effective redshifts, namely, DM/rd (z = 0.70) = 17.96 ± 0.51, DH/rd (z = 0.70) = 21.22 ± 1.20, fσ8 (z = 0.70) = 0.43 ± 0.05, and DM/rd (z = 0.845) = 18.90 ± 0.78, DH/rd (z = 0.845) = 20.91 ± 2.86, fσ8 (z = 0.845) = 0.30 ± 0.08. Combined with BAO measurements including those from the eBOSS DR16 QSO and Lyman-α sample, our measurement has raised the significance level of a non-zero ΩΛ to ∼11σ. The data product of this work is publicly available at https://github.com/icosmology/eBOSS_DR16_LRGxELG and https://www.sdss.org/science/final-bao-and-rsd-measurements/.

scholarly journals Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

2021 ◽  
Author(s):  
Robin E Upham ◽  
Michael L Brown ◽  
Lee Whittaker
Keyword(s):  
Power Spectrum ◽  
Random Noise ◽  
Power Spectra ◽  
Stage Iv ◽  
Wishart Distribution ◽  
Weak Lensing ◽  
Dependence Structure ◽  
Gaussian Fields ◽  
Non Gaussian ◽  
Parameter Constraints

Abstract We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.

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