Two-dimensional spectral representation of periodic, cyclostationary, and more general random processes

2002 ◽  
Author(s):  
Therrien ◽  
Cristi
Keyword(s):  
Spectral Representation ◽  
Random Processes ◽  
Two Dimensional

Analysis of the TiO2 Nanotubes Structure Ordering in the Correlation-Spectral Representation

2018 ◽  
Vol 386 ◽  
pp. 353-358
Author(s):  
Pavel Titov ◽  
Svetlana Shchegoleva ◽  
Nikolai B. Kondrikov
Keyword(s):  
Anodic Oxidation ◽  
Autocorrelation Function ◽  
Spectral Representation ◽  
Fourier Spectrum ◽  
Aqueous Electrolytes ◽  
Two Dimensional ◽  
Quantitative Estimates ◽  
Surface Active ◽  
Structure Ordering

In the paper, the array ordering of the TiO2nanotubes obtained by method of the anodic oxidation in different modes in the fluorine-containing aqueous-non-aqueous electrolytes containing glycerin as well as the surface-active reagents is considered. It was shown that such characteristics as the two-dimensional Fourier-spectrum, autocorrelation function and its spectrum allow us to identify the ordering nature and to obtain the preliminary quantitative estimates of SEM order.

scholarly journals Spectral Analysis of Sampled Signals in the Linear Canonical Transform Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Bing-Zhao Li ◽  
Tian-Zhou Xu
Keyword(s):  
Spectral Analysis ◽  
Spectral Representation ◽  
Digital Signal ◽  
Sampling Theorem ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Two Dimensional ◽  
Research Papers ◽  
One Dimensional ◽  
Uniform Sampling

The spectral analysis of uniform or nonuniform sampling signal is one of the hot topics in digital signal processing community. Theories and applications of uniformly and nonuniformly sampled one-dimensional or two-dimensional signals in the traditional Fourier domain have been well studied. But so far, none of the research papers focusing on the spectral analysis of sampled signals in the linear canonical transform domain have been published. In this paper, we investigate the spectrum of sampled signals in the linear canonical transform domain. Firstly, based on the properties of the spectrum of uniformly sampled signals, the uniform sampling theorem of two dimensional signals has been derived. Secondly, the general spectral representation of periodic nonuniformly sampled one and two dimensional signals has been obtained. Thirdly, detailed analysis of periodic nonuniformly sampled chirp signals in the linear canonical transform domain has been performed.

Compact Probabilistic Representation of Random Processes

1982 ◽  
Vol 49 (4) ◽  
pp. 871-876 ◽  
Author(s):  
S. F. Masri ◽  
R. K. Miller
Keyword(s):  
Random Vibration ◽  
Random Processes ◽  
System Response ◽  
Two Dimensional ◽  
Probabilistic Representation ◽  
Simple Analytical Expression ◽  
Orthogonal Functions ◽  
Covariance Kernel ◽  
Transmission Properties ◽  
Transmission Studies

A method is given for representing analytically defined or data-based covariance kernels of arbitrary random processes in a compact form that results in simplified, analytical, random-vibration transmission studies. The method uses two-dimensional orthogonal functions to represent the covariance kernel of the underlying random process. Such a representation leads to a relatively simple analytical expression for the covariance kernel of the linear system response which consists of two independent groups of terms: one reflecting the input characteristics, and the other accounting for the transmission properties of the excited dynamic system. The utility of the method is demonstrated by application to a covariance kernel widely used in random-vibration studies.

scholarly journals The five-point non-coherent model of a distributed radar object providing the independent control of angle noise probability characteristics along two orthogonal coordinate axes

2021 ◽  
Vol 2134 (1) ◽  
pp. 012003
Author(s):  
A O Podkopayev ◽  
M A Stepanov
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Random Processes ◽  
Radar Target ◽  
Two Dimensional ◽  
Independent Control ◽  
Noise Parameters ◽  
Fixed Model

Abstract The two-dimensional five-point non-coherent model replacing a distributed radar target is explored in this work. Four fixed model points are set in corners of the square but the fifth movable point lies inside of this square. Model points are supplied by normal uncorrelated random processes. The possibilities of the five-point non-coherent model of a distributed radar object for independent control of the producing angle noise parameters along two orthogonal coordinate axes are explored. The disadvantage of this model is noted - the connection of parameters values of angle noise probability density function for two coordinate axes. The expression describing this connection is specified. Expressions determining the boundaries of the allowable coordinate values of the fifth movable point of the five-point non-coherent model, within which the model provides the set parameters of the angle noise probability density function, are defined. The arrived results are validated by program simulations.

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