Spectral Analysis of the Truncated Hilbert Transform with Overlap [PDF]
SIAM Journal on Mathematical Analysis, 2014 We study a restriction of the Hilbert transform as an operator $H_T$ from $L^2(a_2,a_4)$ to $L^2(a_1,a_3)$ for real numbers $a_1 < a_2 < a_3 < a_4$. The operator $H_T$ arises in tomographic reconstruction from limited data, more precisely in the method of differentiated back-projection (DBP).
Reema Al‐Aifari, Alexander Katsevich
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Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: Comparison study with detrended fluctuation analysis and wavelet leaders [PDF]
Physical review. E, Statistical, nonlinear, and soft matter physics, 2011 In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically
Yongxiang Huang +5 more
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A confidence limit for the empirical mode decomposition and Hilbert spectral analysis [PDF]
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2003 The confidence limit is a standard measure of the accuracy of the result in any statistical analysis. Most of the confidence limits are derived as follows. The data are first divided into subsections and then, under the ergodic assumption, the temporal mean is substituted for the ensemble mean.
N. Huang +6 more
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An amplitude-frequency study of turbulent scaling intermittency using Empirical Mode Decomposition and Hilbert Spectral Analysis [PDF]
, 2008 Hilbert-Huang transform is a method that has been introduced recently to decompose nonlinear, nonstationary time series into a sum of different modes, each one having a characteristic frequency.
Yongxiang Huang +3 more
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Comparison between traditional fast Fourier transform and marginal spectra using the Hilbert–Huang transform method for the broadband spectral analysis of the electroencephalogram in healthy humans [PDF]
Engineering Reports, 2021 The fast Fourier transform (FFT) has been the main tool for electroencephalographic (EEG) Spectral Analysis (SPA). However, as the EEG dynamics show nonlinear and non‐stationary behavior, results using the FFT approach may result meaningless.
Eduardo Arrufat‐Pié +5 more
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Topics in Hilbert Spaces, Spectral Theory, and Harmonic Analysis
, 2019 22 ...
Sawyer Jack Robertson
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Koopman spectral analysis of skew-product dynamics on Hilbert $C^*$-modules
, 2023 We introduce a linear operator on a Hilbert $C^*$-module for analyzing skew-product dynamical systems. The operator is defined by composition and multiplication. We show that it admits a decomposition in the Hilbert $C^*$-module, called eigenoperator decomposition, that generalizes the concept of the eigenvalue decomposition.
Dimitrios Giannakis +4 more
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TBA equations and resurgent Quantum Mechanics
Journal of High Energy Physics, 2019 We derive a system of TBA equations governing the exact WKB periods in one-dimensional Quantum Mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE/IM correspondence, and they can be regarded as the solution
Katsushi Ito +2 more
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Hilbert–Huang Spectral Analysis of Cavity Flows Incorporating Fluidic Spoilers
AIAA Journal, 2022 Numerical aeroacoustic analysis was conducted on an M219 cavity geometry, incorporating signature suppression features and leading-edge fluidic spoilers. The numerical model was validated against existing experimental data. The palliative properties of fluidic spoilers were investigated at Mach numbers of 0.85, 1.20, and 1.80 with blowing coefficients
David Bacci, A. J. Saddington
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Hilbert C*-modules and spectral analysis of many-body systems
, 2008 We study the spectral properties of a class of many channel Hamiltonians which contains those of systems of particles interacting through k-body and field type forces which do not preserve the number of particles. Our results concern the essential spectrum, the Mourre estimate, and the absence of singular continuous spectrum.
Mondher Damak, Vladimir Georgescu
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