Correntropy for Random Processes: Properties and Applications in Signal Processing

2010 ◽  
pp. 415-455
Author(s):  
Puskal Pokharel ◽  
Ignacio Santamaria ◽  
Jianwu Xu ◽  
Kyu-hwa Jeong ◽  
Weifeng Liu
Keyword(s):  
Signal Processing ◽  
Random Processes

scholarly journals Reducing of noise structure influence on an accuracy of a desired signal extraction

2018 ◽  
Vol 15 (3) ◽  
pp. 365-370 ◽  
Author(s):  
Vladimir Marchuk
Keyword(s):  
Signal Processing ◽  
Mathematical Expectation ◽  
Random Processes ◽  
Parameters Estimation ◽  
Signal Extraction ◽  
Scientific Contribution ◽  
Noise Component ◽  
Component Structure ◽  
Noise Structure ◽  
Theoretical Results

In the paper, the issues regarding the analysis of the noise component structure are addressed and methods for reducing the error in estimating of the mathematical expectation of the noise component are proposed. The use of the proposed method of ?noise purification? makes possibility to reduce the error introduced by the noise structure when estimating the mathematical expectation and dispersion of the noise component during research. The main scientific contribution in this paper in accuracy increasing of random processes parameters estimation. These theoretical results can be applied in different spheres of data analyzing and signal processing when random processes have some structure.

scholarly journals Linear-logical decision-making algorithm for signal processing

2019 ◽  
Vol 18 (4) ◽  
pp. 385-391
Author(s):  
V. S. Plaksienko
Keyword(s):  
Decision Making ◽  
Signal Processing ◽  
A Priori ◽  
Random Processes ◽  
Considerable Uncertainty ◽  
Discrete Signals ◽  
Mathematical Algorithms ◽  
Analog Form ◽  
Processing Algorithms ◽  
A Priori Uncertainty

Introduction. Heuristic synthesis is used to improve the efficiency of reception and processing of discrete signals under aprior information pressure. The analysis of the decisionmaking algorithm for the linear-logical processing of discrete signals in case of the incomplete aprior data on their parameters is presented. The work objective is to develop and analyze the efficiency of the linear-logical algorithms.Materials and Methods. New mathematical algorithms for the signal reception and processing, effective under conditions of a priori uncertainty, are proposed. They are based on the consideration of the structure of emissions and process exceedance in the signal processing channels.Research Results. Linear-logical algorithms for processing discrete signals are developed. They are based on the consideration of one, two and more detailed characteristics of emissions or exceedance of random processes.Discussion and Conclusion. The results obtained can be useful in the synthesis of algorithms and devices for the signal reception and processing. Algorithms and devices are implemented both in an analog form and in the form of algorithms for computers. The simulation programs for the signal processing under conditions of the considerable uncertainty of aprior information on the signals and the channels of their distribution are developed.

scholarly journals From subgaussianity to stochastic approximation and modelling

2020 ◽  
pp. 84-88
Author(s):  
A. Ya. Olenko
Keyword(s):  
Signal Processing ◽  
Stochastic Approximation ◽  
Sampling Method ◽  
Random Variables ◽  
Research Direction ◽  
Random Processes ◽  
Modern Theory ◽  
Processing Theory ◽  
Research Schools ◽  
Wavelet Decompositions

The modern theory of subgaussian random variables and processes was created by independent efforts of several research schools from France, USA and Ukraine. Professor Yu.Kozachenko was a founder and leading figure of this research direction of the Ukrainian probability school. An outline of Professor Yu.Kozachenko's contribution to the theory of sub-Gaussian random variables and processes is presented. The class of $\varphi$-subgaussian random variables is introduced and its key property is discussed. Then it is demonstrated how these results can be used in stochastic approximation and modeling. In particular, applications to approximation of trajectories of $\varphi$-subgaussian random processes with given accuracy and reliability are discussed. Two important clases of algorithms from the signal processing theory, the Shannon sampling method and wavelet decompositions, are used as examples. Some personal memories of the author about Yu. Kozachenko are included at the end of the paper.

A signal processing method for circular arrays

Geophysics ◽  
1979 ◽  
Vol 44 (2) ◽  
pp. 179-184 ◽  
Author(s):  
John D. Henstridge
Keyword(s):  
Signal Processing ◽  
Random Processes ◽  
Processing Method ◽  
Circular Array ◽  
Directional Information ◽  
Circular Arrays ◽  
Signal Processing Method ◽  
Exploration Seismology ◽  
Spectral Representations ◽  
Stationary Random Processes

The theory of spectral representations of stationary random processes can be a useful tool in signal processing. Using this theory, it is possible to derive simple methods of estimating the phase velocity of surface waves from observations made with a circular array. The methods are totally nondirectional, thus allowing the use of microseisms for exploration seismology. Furthermore, the methods can be extended to yield directional information about both correlated and uncorrelated signals.

Sparse Image and Signal Processing

2009 ◽  
Author(s):  
Jean-Luc Starck ◽  
Fionn Murtagh ◽  
Jalal Fadili
Keyword(s):  
Signal Processing
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