Improving the Accuracy of Quasiclassical Mapping Hamiltonian Methods by Treating the Window Function Width as an Adjustable Parameter

2020 ◽  
Vol 124 (52) ◽  
pp. 11006-11016
Author(s):  
Xing Gao ◽  
Eitan Geva
Keyword(s):  
Adjustable Parameter ◽  
Window Function ◽  
Hamiltonian Methods

scholarly journals Abundance of Primordial Black Holes in Peak Theory for an Arbitrary Power Spectrum

2020 ◽  
Author(s):  
Chul-Moon Yoo ◽  
Tomohiro Harada ◽  
Shin’ichi Hirano ◽  
Kazunori Kohri
Keyword(s):  
Mass Spectrum ◽  
Power Spectrum ◽  
Environmental Effect ◽  
Window Function ◽  
Radial Coordinate ◽  
Primordial Black Holes ◽  
Scale Invariant ◽  
Curvature Perturbation ◽  
Arbitrary Power ◽  
Nonlinear Relation

Abstract We modify the procedure to estimate PBH abundance proposed in Ref. [1] so that it can be applied to a broad power spectrum such as the scale-invariant flat power spectrum. In the new procedure, we focus on peaks of the Laplacian of the curvature perturbation △ ζ and use the values of △ ζ and △ △ ζ at each peak to specify the profile of ζ as a function of the radial coordinate while the values of ζ and △ ζ are used in Ref. [1]. The new procedure decouples the larger-scale environmental effect from the estimate of PBH abundance. Because the redundant variance due to the environmental effect is eliminated, we obtain a narrower shape of the mass spectrum compared to the previous procedure in Ref. [1]. Furthermore, the new procedure allows us to estimate PBH abundance for the scale-invariant flat power spectrum by introducing a window function. Although the final result depends on the choice of the window function, we show that the k-space tophat window minimizes the extra reduction of the mass spectrum due to the window function. That is, the k-space tophat window has the minimum required property in the theoretical PBH estimation. Our procedure makes it possible to calculate the PBH mass spectrum for an arbitrary power spectrum by using a plausible PBH formation criterion with the nonlinear relation taken into account.

scholarly journals Continuous window functions for NFFT

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Daniel Potts ◽  
Manfred Tasche
Keyword(s):  
Fourier Transform ◽  
Shape Parameter ◽  
Optimal Choice ◽  
Approximate Algorithm ◽  
Window Function ◽  
Truncation Parameter ◽  
Error Constant ◽  
Window Functions ◽  
Nonequispaced Fast Fourier Transform ◽  
Error Behavior

AbstractIn this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. Here, we consider the continuous Kaiser–Bessel, continuous exp-type, sinh-type, and continuous cosh-type window functions with the same support and same shape parameter. We present novel explicit error estimates for NFFT with such a window function and derive rules for the optimal choice of the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter. For the considered continuous window functions, the error constants have an exponential decay with respect to the truncation parameter.

scholarly journals Spectral Domain Sparse Representation for DOA Estimation of Signals with Large Dynamic Range

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5164
Author(s):  
Jacob Compaleo ◽  
Inder J. Gupta
Keyword(s):  
Sparse Representation ◽  
Antenna Array ◽  
Dynamic Range ◽  
Direction Of Arrival ◽  
Doa Estimation ◽  
Single Step ◽  
Window Function ◽  
Spectral Domain ◽  
Low Sidelobe ◽  
Weighting Window

Recently, we proposed a Spectral Domain Sparse Representation (SDSR) approach for the direction-of-arrival estimation of signals incident to an antenna array. In the approach, sparse representation is applied to the conventional Bartlett spectra obtained from snapshots of the signals received by the antenna array to increase the direction-of-arrival (DOA) estimation resolution and accuracy. The conventional Bartlett spectra has limited dynamic range, meaning that one may not be able to identify the presence of weak signals in the presence of strong signals. This is because, in the conventional Bartlett spectra, uniform weighting (window) is applied to signals received by various antenna elements. Apodization can be used in the generation of Bartlett spectra to increase the dynamic range of the spectra. In Apodization, more than one window function is used to generate different portions of the spectra. In this paper, we extend the SDSR approach to include Bartlett spectra obtained with Apodization and to evaluate the performance of the extended SDSR approach. We compare its performance with a two-step SDSR approach and with an approach where Bartlett spectra is obtained using a low sidelobe window function. We show that an Apodization Bartlett-based SDSR approach leads to better performance with just single-step processing.

Anisotropic molecules forming a monomolecular layer on a strongly adhesive substrate: a scaled particle treatment

1983 ◽  
Vol 61 (12) ◽  
pp. 1592-1598
Author(s):  
M. Banville ◽  
A. Caillé
Keyword(s):  
Fatty Acids ◽  
Surface Pressure ◽  
Adjustable Parameter ◽  
Scaled Particle Theory ◽  
Long Chain Fatty Acids ◽  
Monomolecular Layer ◽  
Aromatic Molecules ◽  
Simplifying Assumptions ◽  
Long Chain ◽  
Chain Fatty Acids

Long chain fatty acids and large, rigid, aromatic molecules form a monomolecular layer on the surface of clean mercury. The surface pressure isotherms of these systems have been measured previously. In this paper, the scaled particle theory is applied to such monolayers with a number of simplifying assumptions. With a single adjustable parameter, the interaction of the molecules with the substrate and the general features of the surface pressure isotherms of the long chain fatty acids, anthracene, naphthalene, and cholesterol at intermediate liquid densities are fairly well reproduced.

An analysis of the spectrum of a gravity anomaly over an inclined dike

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1500-1501
Author(s):  
B. N. P. Agarwal ◽  
D. Sita Ramaiah
Keyword(s):  
Fourier Transform ◽  
Gravity Anomaly ◽  
Fourier Spectrum ◽  
Fourier Transforms ◽  
Weighted Average ◽  
Window Function ◽  
Average Spectrum ◽  
Amplitude Spectra ◽  
Distance Data ◽  
The Fourier Transform

Bhimasankaram et al. (1977) used Fourier spectrum analysis for a direct approach to the interpretation of gravity anomaly over a finite inclined dike. They derived several equations from the real and imaginary components and from the amplitude and phase spectra to relate various parameters of the dike. Because the width 2b of the dike (Figure 1) appears only in sin (ωb) term—ω being the angular frequency—they determined its value from the minima/zeroes of the amplitude spectra. The theoretical Fourier spectrum uses gravity field data over an infinite distance (length), whereas field observations are available only for a limited distance. Thus, a set of observational data is viewed as a product of infinite‐distance data with an appropriate window function. Usually, a rectangular window of appropriate distance (width) and of unit magnitude is chosen for this purpose. The Fourier transform of the finite‐distance and discrete data is thus represented by convolution operations between Fourier transforms of the infinite‐distance data, the window function, and the comb function. The combined effect gives a smooth, weighted average spectrum. Thus, the Fourier transform of actual observed data may differ substantially from theoretic data. The differences are apparent for low‐ and high‐frequency ranges. As a result, the minima of the amplitude spectra may change considerably, thereby rendering the estimate of the width of the dike unreliable from the roots of the equation sin (ωb) = 0.

scholarly journals Primordial black holes and uncertainties in the choice of the window function

2018 ◽  
Vol 97 (10) ◽  
Author(s):  
Kenta Ando ◽  
Keisuke Inomata ◽  
Masahiro Kawasaki
Keyword(s):  
Black Holes ◽  
Window Function ◽  
Primordial Black Holes
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