scholarly journals Applying Haar Wavelets in Tasks of Digital Processing of Two-Dimensional Signals

2020 ◽  
Vol 9 (6) ◽  
pp. 163-166
Keyword(s):  
System Application ◽  
Physical Nature ◽  
Digital Processing ◽  
Basis Functions ◽  
Haar Wavelets ◽  
Spectral Energy ◽  
Two Dimensional ◽  
Local Basis

In this article, a system application of local basis functions discussed, defined on compact media.Applying formulas for estimating the accuracy of calculating the spectral energy by the method of two-dimensional Haar wavelets and main concepts of Haar fast transformation, spectral energy of Haar coefficients will be discussed in this article. Their effectiveness will be shown in order to solve problems of sampling of compact signals. Signals cannot only be functions of time, defined at finite intervals, but also functions of arguments of a different physical nature, for example, distances along surfaces.

Two-dimensional empirical mode decomposition by finite elements

2006 ◽  
Vol 462 (2074) ◽  
pp. 3081-3096 ◽  
Author(s):  
Y Xu ◽  
B Liu ◽  
J Liu ◽  
S Riemenschneider
Keyword(s):  
Finite Element ◽  
Linear Combination ◽  
Empirical Mode Decomposition ◽  
Spline Interpolation ◽  
Basis Functions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Mode Decomposition

Empirical mode decomposition (EMD) is a powerful tool for analysis of non-stationary and nonlinear signals, and has drawn significant attention in various engineering application areas. This paper presents a finite element-based EMD method for two-dimensional data analysis. Specifically, we represent the local mean surface of the data, a key step in EMD, as a linear combination of a set of two-dimensional linear basis functions smoothed with bi-cubic spline interpolation. The coefficients of the basis functions in the linear combination are obtained from the local extrema of the data using a generalized low-pass filter. By taking advantage of the principle of finite-element analysis, we develop a fast algorithm for implementation of the EMD. The proposed method provides an effective approach to overcome several challenging difficulties in extending the original one-dimensional EMD to the two-dimensional EMD. Numerical experiments using both simulated and practical texture images show that the proposed method works well.

Exact third-order structure functions for two-dimensional turbulence

2018 ◽  
Vol 851 ◽  
pp. 672-686 ◽  
Author(s):  
Jin-Han Xie ◽  
Oliver Bühler
Keyword(s):  
Structure Functions ◽  
Spectral Energy ◽  
Order Structure ◽  
Two Dimensional ◽  
Third Order ◽  
Transfer Rates ◽  
The Third ◽  
Random Forcing ◽  
Asymptotic Expressions ◽  
Special Case

We derive and investigate exact expressions for third-order structure functions in stationary isotropic two-dimensional turbulence, assuming a statistical balance between random forcing and dissipation both at small and large scales. Our results extend previously derived asymptotic expressions in the enstrophy and energy inertial ranges by providing uniformly valid expressions that apply across the entire non-dissipative range, which, importantly, includes the forcing scales. In the special case of white noise in time forcing this leads to explicit predictions for the third-order structure functions, which are successfully tested against previously published high-resolution numerical simulations. We also consider spectral energy transfer rates and suggest and test a simple robust diagnostic formula that is useful when forcing is applied at more than one scale.

scholarly journals Two-Dimensional, Time-dependent Modelling of an Arbitrarily Shaped Ice Mass with the Finite-Element Technique

1985 ◽  
Vol 31 (109) ◽  
pp. 350-359 ◽  
Author(s):  
Steven M. Hodge
Keyword(s):  
Finite Element ◽  
Numerical Models ◽  
Basis Functions ◽  
Time Dependent ◽  
Small Computer ◽  
Two Dimensional ◽  
Maximum Increase ◽  
Steady State Condition ◽  
Finite Element Technique ◽  
Element Technique

AbstractThe two-dimensional, time-dependent flow of an arbitrarily shaped ice mass can be successfully modeled with the finite-element technique on a small computer. Methods developed for automatically generating the mesh data greatly simplify the data preparation and optimize the numerical simulations. Using quadratic basis functions permits the flow to be approximated quite adequately by only two element rows (five nodes vertically). Mixed-order basis functions, however, must be used so that numerical oscillations do not set in, and the ends of the ice mass, where the thickness tends to zero, must be treated carefully. Time simulations to a steady-state condition are necessary to test such numerical models adequately.South Cascade Glacier, Washington, is currently close to equilibrium. A bedrock sill dominates the bed topography in the lower half of the glacier, rising to a height of about 20% of the ice thickness. This sill produces a maximum increase in the overall thickness of about 6–7% compared to what the thickness would have been if the sill were not present. Finally, this glacier does not appear to be sliding much, if at all, despite its maritime alpine environment. This could help explain the difficulties encountered when trying to measure sliding and basal water pressures on the same glacier (Hodge, 1979), or it could imply that drag exerted by the valley walls has a significantly greater effect than conventional shape-factor concepts imply.

Optical Digital Processing Of Two-Dimensional Digital Data

1977 ◽  
Author(s):  
T. K. Gaylord ◽  
R. Magnusson ◽  
J. E. Weaver
Keyword(s):  
Digital Processing ◽  
Digital Data ◽  
Two Dimensional
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