scholarly journals WAVE GROUP ANALYSIS BY THE HILBERT TRANSFORM

1988 ◽  
Vol 1 (21) ◽  
pp. 66 ◽  
Author(s):  
Robert T. Hudspeth ◽  
Josep R. Medina
Keyword(s):  
Hilbert Transform ◽  
Group Analysis ◽  
Height Function ◽  
Sea Surface ◽  
Frequency Function ◽  
Wave Group ◽  
Transform Method ◽  
Wave Groups ◽  
The Mean ◽  
The Hilbert Transform

A methodology based on linear theory is presented for analyzing wave groups from a random sea representation in the complex plane. A wave height function [H(t)], a local frequency function, [0(t)] , and an orbital velocity function [V(t)] are defined from the Hilbert transform of the sea surface elevation. Envelopes computed by the Hilbert transform are compared with the SIWEH. A three axes representation of the mean lengths of runs of waves is employed to compare the lengths of runs computed by the discrete wave method with runs computed by the Hilbert transform method.

scholarly journals PORTRAIT AND HILBERT TRANSFORM METHODS FOR EVALUATING CONTINUOUS RELATIVE PHASE BETWEEN LOWER-LIMB JOINTS IN THE ELDERLY DURING WALKING

2021 ◽  
pp. 2140038
Author(s):  
HYUK-JAE CHOI ◽  
GYOOSUK KIM ◽  
CHANG-YONG KO
Keyword(s):  
Angular Velocity ◽  
Hilbert Transform ◽  
Lower Limb ◽  
Cross Correlation ◽  
Relative Phase ◽  
The Elderly ◽  
Transform Method ◽  
Transform Methods ◽  
Continuous Relative Phase ◽  
The Hilbert Transform

In order to calculate the continuous relative phase (CRP) between joints, the portrait method based on the joint angle and angular velocity and the Hilbert transform method based on the analytical signal have been widely used. However, there are few comparisons of these methods. Therefore, the aim of this study is to quantitatively compare these methods by calculating the CRP in the lower-limb joints of the elderly during level free walking. Eighteen elderly female adults ([Formula: see text] year-old, [Formula: see text][Formula: see text]cm, [Formula: see text][Formula: see text]kg) wearing a Helen Hayes full-body marker set walked 10[Formula: see text]m on level ground at a self-selected velocity. The angles of the hip, knee, and ankle were measured. To calculate the CRP using the portrait method, the angular velocities were measured. Then, the phases between the angle and the angular velocity were calculated. To calculate the CRP using the Hilbert transform method, analytical signals were acquired. Then, the phases between the real and imaginary parts were calculated. A CRP was calculated as the difference between the phase in the proximal joint and the phase in the distal joint. To evaluate the similarity in the shape between the portrait and Hilbert transform methods, the cross-correlation was calculated. Bland–Altman plot analyses were performed to assess the agreement between these methods. For the root mean squares (RMSs) and standard deviations (SDs), a paired [Formula: see text]-test and the Pearson correlation between methods were evaluated. There were similarities in the in-phase or out-of-phase features and in the RMS and SD between the methods. Additionally, a higher cross-correlation and agreement between them were found. These results indicated the similarity between the portrait and Hilbert transform methods for the calculation of the CRP. Therefore, either method can be used to evaluate joint coordination.

Time-Varying and Non-Linear Dynamical System Identification Using the Hilbert Transform

2005 ◽  
Author(s):  
Michael Feldman
Keyword(s):  
Hilbert Transform ◽  
Special Kind ◽  
Harmonic Signal ◽  
Dynamic Structure ◽  
Forced Vibrations ◽  
Time Varying ◽  
Transform Method ◽  
Non Linear ◽  
Force Signal ◽  
The Hilbert Transform

The objective of the paper is to explain a modern Hilbert transform method for analysis and identification of mechanical non-linear vibration structures in the case of quasiperiodic signals. This special kind of periodicity arises in experimental vibration signals. The method is based on the Hilbert transform of input and output signals in a time domain to extract the instantaneous dynamic structure characteristics. The paper focuses on the dynamic analysis and identification of three groups of dynamics systems: • Forced vibrations of linear and non-linear SDOF systems excited with quasiperiodic force signal. • Combined forced vibrations of quasiperiodic time varying linear and non-linear SDOF systems excited with harmonic signal. • Combined self-excited and forced vibrations of non-linear SDOF systems excited with harmonic signal. The study focuses on signal processing techniques for nonlinear system investigation, which enable us to estimate instantaneous system dynamic parameters (natural frequencies, damping characteristics and their dependencies on a vibration amplitude and frequency) for different kinds of system excitation.

Non-Gaussian Wave Groups Generated in an Offshore Wave Basin and Their Statistics

2011 ◽  
Author(s):  
Zhivelina Cherneva ◽  
C. Guedes Soares
Keyword(s):  
Wave Groups ◽  
Wave Basin ◽  
Lower Envelopes ◽  
The Mean ◽  
Wave Maker ◽  
Using Data ◽  
Non Gaussian ◽  
Offshore Wave ◽  
The Hilbert Transform ◽  
Theoretical Results

The main goal of this work is to investigate the wave groups using data from a deep water basin. Available data are for unidirectional waves measured at several fixed points situated in different distances from the wave maker. Previous works of many authors show that such series describe a process which differs significantly from the Gaussian one. Omitting the usual envelope definition by the Hilbert transform an upper and lower envelopes are introduced. Then the mean high run, mean group length and their distributions are found and compared with the theoretical results for Gaussian process.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

A Bayesian View on the Hilbert Transform and the Kramers-Kronig Transform of Electrochemical Impedance Data: Probabilistic Estimates and Quality Scores

2020 ◽  
Author(s):  
Jiapeng Liu ◽  
Ting Hei Wan ◽  
Francesco Ciucci
Keyword(s):  
Power Generation ◽  
Electrochemical Impedance Spectroscopy ◽  
Hilbert Transform ◽  
Electrochemical Impedance ◽  
The Self ◽  
Impedance Data ◽  
The Hilbert Transform ◽  
Validation Tests ◽  
Self Consistency ◽  
Mathematical Relations

<p>Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental tools in electrochemistry and has applications ranging from energy storage and power generation to medicine. Considering the broad applicability of the EIS technique, it is critical to validate the EIS data against the Hilbert transform (HT) or, equivalently, the Kramers–Kronig relations. These mathematical relations allow one to assess the self-consistency of obtained spectra. However, the use of validation tests is still uncommon. In the present article, we aim at bridging this gap by reformulating the HT under a Bayesian framework. In particular, we developed the Bayesian Hilbert transform (BHT) method that interprets the HT probabilistic. Leveraging the BHT, we proposed several scores that provide quick metrics for the evaluation of the EIS data quality.<br></p>

scholarly journals A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 65
Author(s):  
Benjamin Akers ◽  
Tony Liu ◽  
Jonah Reeger
Keyword(s):  
Radial Basis Function ◽  
Hilbert Transform ◽  
Basis Function ◽  
Differential Operators ◽  
Convergence Rates ◽  
Traveling Wave Solutions ◽  
Algebraic Decay ◽  
Pseudo Differential Operators ◽  
Radial Basis ◽  
The Hilbert Transform

A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.

scholarly journals Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1299
Author(s):  
Shengli Lv
Keyword(s):  
Steady State ◽  
Transient State ◽  
Repairable System ◽  
Repair Rate ◽  
Numerical Illustration ◽  
Transform Method ◽  
Unreliable Server ◽  
Busy Time ◽  
The Mean ◽  
Mean Time

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

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