scholarly journals ConceFT: concentration of frequency and time via a multitapered synchrosqueezed transform

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150193 ◽  
Author(s):  
Ingrid Daubechies ◽  
Yi (Grace) Wang ◽  
Hau-tieng Wu
Keyword(s):  
Theoretical Analysis ◽  
Numerical Experiments ◽  
Time Dependent ◽  
New Method ◽  
Time Varying ◽  
Frequency Content ◽  
Time Frequency ◽  
Instantaneous Frequencies

A new method is proposed to determine the time–frequency content of time-dependent signals consisting of multiple oscillatory components, with time-varying amplitudes and instantaneous frequencies. Numerical experiments as well as a theoretical analysis are presented to assess its effectiveness.

scholarly journals A Simpler GMRES Method for Oscillatory Integrals with Irregular Oscillations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Qinghua Wu ◽  
Meiying Xiang
Keyword(s):  
Theoretical Analysis ◽  
Matrix Factorization ◽  
Numerical Experiments ◽  
Oscillatory Integral ◽  
Oscillatory Integrals ◽  
New Method ◽  
Gmres Method ◽  
Hessenberg Matrix

A simpler GMRES method for computing oscillatory integral is presented. Theoretical analysis shows that this method is mathematically equivalent to the GMRES method proposed by Olver (2009). Moreover, the simpler GMRES does not require upper Hessenberg matrix factorization, which leads to much simpler program and requires less work. Numerical experiments are conducted to illustrate the performance of the new method and show that in some cases the simpler GMRES method could achieve higher accuracy than GMRES.

A Correlative Method of Machine Condition Monitoring Based on the Choi-Williams Distribution

2005 ◽  
Vol 293-294 ◽  
pp. 777-784
Author(s):  
Guoan Yang ◽  
Zhenhuan Wu ◽  
Jin Ji Gao
Keyword(s):  
Fault Diagnosis ◽  
Correlation Analysis ◽  
Condition Monitoring ◽  
New Method ◽  
Time Varying ◽  
Machine Condition ◽  
Time Frequency ◽  
Machine Condition Monitoring ◽  
Machine Fault Diagnosis ◽  
Feature Extractor

In this paper, a new method for time-varying machine condition monitoring is proposed. By Choi-Williams distribution, the interference terms produced by the bilinear time-frequency transform are reduced and the fault signal is processed by the correlation analysis of the Choi-Williams distribution. For machine fault diagnosis, both the feature extractor and classifier are combined to make a decision. It is particularly suited to those who are not experts in the field. Satisfactory results have been obtained from a real example and the effectiveness of the proposed method is demonstrated.

Multi-Dimensional Directional Spectrograms and Campbell (ZMOD) Diagrams for Rotating Machinery

1995 ◽  
Author(s):  
I. Bucher ◽  
D. J. Ewins ◽  
D. A. Robb ◽  
P. Schmiechen
Keyword(s):  
Rotating Machinery ◽  
Experimental Results ◽  
New Method ◽  
Frequency Content ◽  
Rotating Disc ◽  
Vibration Signals ◽  
Time Frequency ◽  
Spatial Response ◽  
Spatial Domains ◽  
Vibration Pattern

Abstract A new method for decomposition of vibration signals measured on rotating machinery is presented in this paper. The method uses a signal measured from a number of sensors to decompose the spatial response according to the direction of the progression of motion, the frequency content and the various wavelengths. For the simple case of shaft vibration, two sensors, horizontal and vertical, are used to separate the vibration pattern into forward and backward progressing components. For the case of a rotating disc, more sensors are required to further decompose the response into different wavelengths. This allows one to monitor and to identify potentially dangerous vibration patterns exhibiting large backward components. The method is shown to provide better resolution in the time-frequency (speed of rotation) and spatial domains by separating several, usually overlapping patterns. Several analytical and experimental results demonstrate the usefulness of the proposed method.

scholarly journals On preconditioned normal and skew-Hermitian splitting iteration method for continuous Sylvester equations AX + XB = C*

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2207-2217
Author(s):  
Xue-Qing Liang ◽  
Xiang Wang ◽  
Xiao-Bin Tang ◽  
Xiao-Yong Xiao
Keyword(s):  
Exact Solution ◽  
Theoretical Analysis ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Convergence Property ◽  
Positive Definite ◽  
New Method ◽  
Splitting Iteration Method

In this paper, we present a preconditioned normal and skew-Hermitian splitting (PNSS) iteration method for continuous Sylvester equations AX + XB = C with positive definite/semi-definite matrices. Theoretical analysis shows that the PNSS methods will converge unconditionally to the exact solution of the continuous Sylvester equations. An inexact variant of the PNSS iteration method(IPNSS) and the analysis of its convergence property in detail have been established. Numerical experiments further show that this new method is more efficient and robust than the existing ones.

LOCAL HIGH-ORDER ABSORBING BOUNDARY CONDITIONS FOR TIME-DEPENDENT WAVES IN GUIDES

2007 ◽  
Vol 15 (01) ◽  
pp. 1-22 ◽  
Author(s):  
THOMAS HAGSTROM ◽  
MANUELA L. DE CASTRO ◽  
DAN GIVOLI ◽  
DINA TZEMACH
Keyword(s):  
Boundary Conditions ◽  
Numerical Experiments ◽  
Optimal Choice ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Time Dependent ◽  
Time Varying ◽  
Scalar Wave ◽  
Absorbing Boundary ◽  
Free Parameters

The scalar wave equation in a two-dimensional semi-infinite wave guide is considered. The recently proposed Hagstrom–Warburton (H–W) local high-order absorbing boundary conditions (ABCs), which are based on a modification of the Higdon ABCs, are presented in this context. The P-order ABC involves the free parameters 0 < aj ≤ 1, for j = 0, 1, …, P, which have to be chosen. The choice aj = 1 for all j is shown to be satisfactory, in general, although not necessarily optimal. The optimal choice of the parameters is discussed via both theoretical analysis and numerical experiments. In addition, an adaptive scheme which controls the time-varying values of P and aj is presented and tested.

Comparison of wavelet continuous transform and signal averaged ECG for high frequency content and late potential detection in healthy individuals

2020 ◽  
Vol 41 (Supplement_2) ◽  
Author(s):  
D Garcia Iglesias ◽  
J.M Rubin Lopez ◽  
D Perez Diez ◽  
C Moris De La Tassa ◽  
F.J De Cos Juez ◽  
...  
Keyword(s):  
High Frequency ◽  
Classical Method ◽  
Total Power ◽  
Frequency Content ◽  
Healthy Individuals ◽  
Time Frequency ◽  
Qt Intervals ◽  
Long Time ◽  
Power Content ◽  
High Frequency Content

Abstract Introduction The Signal Averaged ECG (SAECG) is a classical method forSudden Cardiac Death (SCD) risk assessment, by means of Late Potentials (LP) in the filtered QRS (fQRS)[1]. But it is highly dependent on noise and require long time records, which make it tedious to use. Wavelet Continuous Transform (WCT) meanwhile is easier to use, and may let us to measure the High Frequency Content (HFC) of the QRS and QT intervals, which also correlates with the risk of SCD [2,3]. Whether the HFC of the QRS and QT measured with the WCT is a possible subrogate of LP, has never been demonstrated. Objective To demonstrate if there is any relationship between the HFC measured with the WCT and the LP analyzed with the SAECG. Methods Data from 50 consecutive healthy individuals. The standard ECG was digitally collected for 3 consecutive minutes. For the WCT Analysis 8 consecutive QT complexes were used and for the SAECG Analysis all available QRS were used. The time-frequency data of each QT complex were collected using the WCT as previously described [3] and the Total, QRS and QT power were obtained from each patient. For the SAECG, bipolar X, Y and Z leads were used with a bidirectional filter at 40 to 250 Hz [1]. LP were defined as less than 0.05 z in the terminal part of the filtered QRS and the duration (SAECG LP duration) and root mean square (SAECG LP Content) of this LP were calculated. Pearson's test was used to correlate the Power content with WCT analysis and the LP in the SAECG. Results There is a strong correlation between Total Power and the SAECG LP content (r=0.621, p&lt;0.001). Both ST Power (r=0.567, p&lt;0.001) and QRS Power (r=0.404, p=0.004) are related with the SAECG LP content. No correlation were found between the Power content (Total, QRS or ST Power) and the SAECG LP duration. Also no correlation was found between de SAECG LP content and duration. Conclusions Total, QRS and ST Power measured with the WCT are good surrogates of SAECG LP content. No correlation were found between WCT analysis and the SAECG LP duration. Also no correlation was found between the SAECG LP content and duration. This can be of high interest, since WCT is an easier technique, not needing long recordings and being less affected by noise. Funding Acknowledgement Type of funding source: None

scholarly journals Integrating Semilinear Wave Problems with Time-Dependent Boundary Values Using Arbitrarily High-Order Splitting Methods

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1113
Author(s):  
Isaías Alonso-Mallo ◽  
Ana M. Portillo
Keyword(s):  
Numerical Experiments ◽  
Splitting Method ◽  
Method Of Lines ◽  
Time Integration ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
High Order ◽  
Time Dependent ◽  
Boundary Values ◽  
Lipschitz Continuous

The initial boundary-value problem associated to a semilinear wave equation with time-dependent boundary values was approximated by using the method of lines. Time integration is achieved by means of an explicit time method obtained from an arbitrarily high-order splitting scheme. We propose a technique to incorporate the boundary values that is more accurate than the one obtained in the standard way, which is clearly seen in the numerical experiments. We prove the consistency and convergence, with the same order of the splitting method, of the full discretization carried out with this technique. Although we performed mathematical analysis under the hypothesis that the source term was Lipschitz-continuous, numerical experiments show that this technique works in more general cases.

ANTICIPATED FUTURE CONSUMPTION IN AN ENDOGENOUS GROWTH MODEL

2020 ◽  
pp. 1-37
Author(s):  
Manuel A. Gómez ◽  
Goncalo Monteiro
Keyword(s):  
Theoretical Analysis ◽  
Endogenous Growth ◽  
Growth Model ◽  
Reference Point ◽  
Time Varying ◽  
Standard Specification ◽  
Equilibrium Dynamics ◽  
Current Consumption ◽  
Endogenous Growth Model ◽  
Future Consumption

We devise an endogenous growth model in which agents’ utility depends not only on current consumption but also on the pleasure of anticipated future consumption. We consider the case in which agents derive satisfaction from their own anticipatory feelings—inward-looking or internal anticipation—and the case in which agents derive utility from anticipation of other people’s future consumption—outward-looking or external anticipation. We characterize the effects of introducing a forward-looking consumption reference on the dynamics of the economy. Whereas the inward-looking economy features transitional dynamics, the outward-looking economy does not. The distortions caused by the externality in the economy with external habits can be corrected by subsidizing income at a time-varying rate or by means of a tax on consumption at a decreasing rate. We contrast the equilibrium dynamics of our specification to the more standard specification of the habit formation consumption reference point. Numerical simulations supplement the theoretical analysis.

A New Method for Phase Difference Estimation Based on Time-Varying Signal Model

2013 ◽  
Vol 333-335 ◽  
pp. 650-655
Author(s):  
Peng Hui Niu ◽  
Yin Lei Qin ◽  
Shun Ping Qu ◽  
Yang Lou
Keyword(s):  
Signal Processing ◽  
Real Time ◽  
Phase Difference ◽  
Time Signal ◽  
Time Interval ◽  
Time Varying ◽  
Signal Model ◽  
Time Frequency ◽  
Mass Flowmeter ◽  
Coriolis Mass Flowmeter

A new signal processing method for phase difference estimation was proposed based on time-varying signal model, whose frequency, amplitude and phase are time-varying. And then be applied Coriolis mass flowmeter signal. First, a bandpass filtering FIR filter was applied to filter the sensor output signal in order to improve SNR. Then, the signal frequency could be calculated based on short-time frequency estimation. Finally, by short window intercepting, the DTFT algorithm with negative frequency contribution was introduced to calculate the real-time phase difference between two enhanced signals. With the frequency and the phase difference obtained, the time interval of two signals was calculated. Simulation results show that the algorithms studied are efficient. Furthermore, the computation of algorithms studied is simple so that it can be applied to real-time signal processing for Coriolis mass flowmeter.

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