Some Studies on Multidimensional Fourier Theory for Hilbert Transform, Analytic Signal and AM–FM Representation
Sign Up to like & getrecommendations! Published in 2019 at "Circuits, Systems, and Signal Processing"
DOI: 10.1007/s00034-019-01133-x
Abstract: In this paper, we propose the notion of Fourier frequency vector (FFV) which is inherently associated with the multidimensional (MD) Fourier representation (FR) of a signal. The proposed FFV provides physical meaning to the so-called… read more here.
Keywords: analytic signal; multidimensional fourier; hilbert transform; representation ... See more keywords
A Remark on the Arcsine Distribution and the Hilbert transform
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Fourier Analysis and Applications"
DOI: 10.1007/s00041-019-09678-w
Abstract: It is known that if $$(p_n)_{n \in \mathbb {N}}$$(pn)n∈N is a sequence of orthogonal polynomials in $$L^2([-1,1], w(x)dx)$$L2([-1,1],w(x)dx), then the roots are distributed according to an arcsine distribution $$\pi ^{-1} (1-x^2)^{-1}dx$$π-1(1-x2)-1dx for a wide variety… read more here.
Keywords: arcsine distribution; remark arcsine; hilbert transform;
Approximation of the Hilbert Transform On The Unit Circle
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-025-03044-3
Abstract: The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegő and anti-Szegő quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accuracy… read more here.
Keywords: hilbert; hilbert transform; transform unit; approximation hilbert ... See more keywords
Oscillatory hyper-Hilbert transform along curves on modulation spaces
Sign Up to like & getrecommendations! Published in 2018 at "Frontiers of Mathematics in China"
DOI: 10.1007/s11464-018-0688-x
Abstract: We consider the boundedness of the n-dimension oscillatory hyper-Hilbert transform along homogeneous curves on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces. The main theorems signicantly improve some known results. read more here.
Keywords: modulation; modulation spaces; transform along; hyper hilbert ... See more keywords
A comparative study for the source depth estimation of very low frequency electromagnetic (VLF-EM) signals
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Applied Geophysics"
DOI: 10.1016/j.jappgeo.2019.01.007
Abstract: Abstract In general, a quantitative interpretation of geophysical data yields information on the nature of subsurface structures of geologic interest besides depth of the source and the associated physical property contrast. However, all geophysical interpretation… read more here.
Keywords: hilbert transform; comparative study; depth; vlf signals ... See more keywords
On using the Hilbert transform for blind identification of complex modes: A practical approach
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Sound and Vibration"
DOI: 10.1016/j.jsv.2017.09.017
Abstract: Abstract The modal identification of dynamical systems under operational conditions, when subjected to wide-band unmeasured excitations, is today a viable alternative to more traditional modal identification approaches based on processing sets of measured FRFs or… read more here.
Keywords: modal identification; using hilbert; complex modes; blind identification ... See more keywords
Hilbert transform-based nonparametric identification of nonlinear ship roll motion under free-roll and irregular wave exciting conditions
Sign Up to like & getrecommendations! Published in 2021 at "Ships and Offshore Structures"
DOI: 10.1080/17445302.2021.1954327
Abstract: This paper presents a numerical investigation of two Hilbert transform (HT)-based nonlinear identification methods to estimate dynamic characteristics of ship roll motions using free-roll response.... read more here.
Keywords: roll; ship roll; free roll; transform based ... See more keywords
Hilbert transform for the three-dimensional Vekua equation
Sign Up to like & getrecommendations! Published in 2018 at "Complex Variables and Elliptic Equations"
DOI: 10.1080/17476933.2018.1555246
Abstract: ABSTRACT The three-dimensional Hilbert transform takes scalar data on the boundary of a domain and produces the boundary value of the vector part of a quaternionic monogenic (hyperholomorphic) function of three real variables, for which… read more here.
Keywords: three dimensional; hilbert transform; vekua equation;
Numerical Hilbert Transform Algorithm for Causal Interpolation of Functions Represented by Cubic and Exponential Splines
Sign Up to like & getrecommendations! Published in 2021 at "IEEE Access"
DOI: 10.1109/access.2021.3117978
Abstract: This paper presents an algorithm for numerical Hilbert transform of functions represented by cubic and exponential splines, which is suitable for causal interpolation of data spanning several frequency decades. It does not suffer from excessive… read more here.
Keywords: hilbert transform; causal interpolation; numerical hilbert;
Bathymetry Determination From Marine Radar Image Sequences Using the Hilbert Transform
Sign Up to like & getrecommendations! Published in 2017 at "IEEE Geoscience and Remote Sensing Letters"
DOI: 10.1109/lgrs.2017.2668383
Abstract: This letter presents an image processing technique based on the theory of the Hilbert transform to determine the coastal bathymetry from marine radar image sequences. Use of the Hilbert transform enables the difficulties and complications… read more here.
Keywords: image; image sequences; hilbert transform; bathymetry ... See more keywords
VHERS: A Novel Variational Mode Decomposition and Hilbert Transform-Based EEG Rhythm Separation for Automatic ADHD Detection
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Instrumentation and Measurement"
DOI: 10.1109/tim.2022.3204076
Abstract: Attention deficit hyperactivity disorder (ADHD) is an isogenous pattern of hyperactivity, impulsivity, and inattention, resulting in disorders like anxiety, disability in learning, and depression. The electroencephalogram (EEG) signals are a valuable source for early detection… read more here.
Keywords: adhd; novel variational; detection; variational mode ... See more keywords