Construction of signal-dependent Cohen's-class time-frequency distributions using iterative blind deconvolution

2003 ◽  
Author(s):  
Andrew E. Yagle ◽  
Jose E. Torres-Fernandez
Keyword(s):  
Blind Deconvolution ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Class Time ◽  
Cohen's Class

scholarly journals Cohen’s Class Time-Frequency Distributions for Measurement Signals as a Means of Monitoring Technological Processes

2019 ◽  
Vol 49 (4) ◽  
pp. 252-256
Author(s):  
D. B. Fedosenkov ◽  
A. A. Simikova ◽  
S. M. Kulakov ◽  
B. A. Fedosenkov
Keyword(s):  
Frequency Distributions ◽  
Time Frequency ◽  
Technological Processes ◽  
Class Time ◽  
Cohen's Class

scholarly journals COHEN’S CLASS TIME-FREQUENCY DISTRIBUTIONS FOR MEASUREMENT SIGNALS AS A MEANS OF MONITORING TECHNOLOGICAL PROCESSES

2019 ◽  
Vol 62 (4) ◽  
pp. 324-329
Author(s):  
D. B. Fedosenkov ◽  
A. A. Simikova ◽  
S. M. Kulakov ◽  
B. A. Fedosenkov
Keyword(s):  
Wigner Distribution ◽  
Bulk Material ◽  
Mathematical Tool ◽  
Distribution Map ◽  
Frequency Distributions ◽  
One Dimensional ◽  
Time Frequency ◽  
Technological Processes ◽  
Class Time ◽  
Cohen's Class

The article presents and describes Cohen’s class time-frequency distributions which are expedient to use as a mathematical tool that allows to create a convenient – in terms of information content and semantic clarity – visual-graphical representation of the opera ting modes of various technological processes including processes of ferrous metallurgy. It was noted that a controlling process is usually implemented without simultaneous visual monitoring of each scalar (one-dimensional) coordinate that is under control, but the presence of such monitoring is an important condition for the computer-aided controlling of the dynamics of non-stationary technological processes. To eliminate this drawback, it was proposed to perform synchronous monitoring using the multidimensional Cohen’s class time-frequency distributions, when each measurement scalar signal is specifically represented through one of these distributions, for example, the Wigner-Ville distribution. An expression is given for the generalized distribution of Cohen’s class with a distribution kernel and an ambiguity function. This function allows receiving distributions of various types from the maternal function. The most typical representatives of time-frequency distributions forming this class are given with their available  kernels. The possibility of appearance of interference elements, which make it difficult to identify the controlled modes, on a signal distribution map is proved. Case of the formation of virtual elements within the Wigner-Ville distribution representing a two-component one-dimensional signal is considered. Te conditions are explained for the emergence of parasitic elements on the distribution map, obtained, for example, during realizing the process of multi-component feeding the bulk blast furnace charge materials in the production of sintering mixture. An analytical expression is obtained for the Wigner distribution, which displays a multi-component scalar signal and contains the information (useful) and virtual (parasitic) parts of the time-frequency distribution. A link between the number of bulk material feeders available in the feeding devices unit and the number of parasitic (virtual) elements in the Wigner distribution was determined. Using the dosing process as an example, the effect of the noise components propagation in the Wigner distribution is demonstrated. An example is given to illustrate the penetration of noise into the Wigner distribution and appearance of the virtual concentration in it when displaying a signal waveform with a noisy pause and two sections with different frequencies. An expression for the Wigner distribution in the form of a comb function is obtained. The conclusion was made about the parameters of the distribution periodicity and the required sampling frequency of measurement signals.

APPLICATION OF COHEN'S CLASS TIME-FREQUENCY DISTRIBUTIONS IN THE BELOUSOV–ZHABOTINSKY REACTION ANALYSIS

2004 ◽  
Vol 14 (10) ◽  
pp. 3679-3688 ◽  
Author(s):  
K. DAROWICKI ◽  
W. FELISIAK
Keyword(s):  
Batch Reactor ◽  
Three Dimensional ◽  
Power Spectra ◽  
Kernel Functions ◽  
Function Parameter ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Class Time ◽  
Cohen's Class ◽  
Belousov Zhabotinsky Reaction

The systematic study of application of Cohen's class time-frequency representations in the analysis of periodic BZ oscillations generated in batch reactor has been presented. Several distributions belonging to Cohen's class have been applied in the analysis of selected signal being the register of bromide selective electrode. Among them were Wigner–Ville, Choi–Williams and cone-shaped distributions. The application of mentioned methods allow instantaneous power spectra to be obtained and simultaneously give the possibility of observing evolution of frequency composition of investigated oscillations. The systematic filtering of signal, using so-called kernel functions, allows to eliminate undesirable cross terms and finally leads to the selection of a suitable method for chemical oscillations decomposition. The results presented in the form of three-dimensional pictures, illustrate the decrease in frequency of oscillations of exponential character. On the basis of the obtained results the cone-shaped distribution for kernel function parameter α=1 has been selected as the best method for Belousov–Zhabotinsky oscillations analysis in joint time-frequency domain.

scholarly journals Determination of the Appropriate Kernel Structure in Electroencephalography Analysis of Alcoholic Subjects

2020 ◽  
Vol 37 (4) ◽  
pp. 571-577
Author(s):  
Omer Akgun
Keyword(s):  
Function Analysis ◽  
Biological Effects ◽  
Neuronal Loss ◽  
Kernel Functions ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Brain Functions ◽  
Cohen's Class ◽  
The Brain

Alcoholism is one of the major health problems in the world. The organ most affected by alcohol is the brain. It has been shown that alcohol causes neuronal loss in the brain and reduces brain blood flow and oxygen use. Electroencephalography is a method that measures the instantaneous electrical activity of the brain. It is known that valuable information can be obtained by observing the biological effects of alcohol through EEG. As their methods of signal processing and analysis have evolved, Electroencephalography signals have attracted the attention of researchers in this field. In this study, methods of the time-frequency analysis were applied to Electroencephalography signals obtained from normal and alcoholic subjects. For this purpose, the Cohen’s class distribution was examined. Ambiguity function analysis, which was in the structure of the distribution, was applied to the signals. Then, from the kernel structure inside the distribution, the Wigner-Ville distribution, which was very common, was reached and this distribution was examined. The inadequacy of the distribution resolution was seen and analysis of the new time-frequency distributions, which were obtained by making convolution with 4 types of kernel functions (nonseparable, separable, Doppler independent, lag independent), was performed. As a result, it was shown that the resolution of time-frequency distributions could be improved with proper kernel functions. Thus, at the end of these analyses, changes that alcohol caused in brain functions were revealed.

scholarly journals Dynamic modal control of unmanned vehicle movement in open pit mining

2021 ◽  
Vol 44 (3) ◽  
pp. 271-284
Author(s):  
I. V. Chicherin ◽  
B. A. Fedosenkov
Keyword(s):  
Wavelet Transforms ◽  
Open Pit ◽  
Open Pit Mining ◽  
Modal Control ◽  
Frequency Distributions ◽  
Unmanned Vehicle ◽  
Time Frequency ◽  
Cohen's Class ◽  
Computer Aided ◽  
Modal Controller

The purpose of this study is to present a number of aspects in the modern concept of computer-aided dynamic modal control of unmanned quarry vehicles in open pit mining. In particular, the software and hardware module that is a part of the “Smart Quarry” global structure deals with the conditions of matching a form of specific current trajectories (their deviation to the left or right of the nominal axial trajectory) to information “trajectory” chirp signals. The study employs the methods of wavelet transforms to convert one-dimensional signals that generate unmanned vehicle current trajectories into the time-frequency distributions of Cohen’s class. The formation of unmanned vehicle current trajectories under their deviation to the left / right from the nominal axial trajectory on straight and curved routes is considered schematically. It is noted that the tracking of unmanned current trajectories on quarry routes is carried out taking into account the nature of trajectory signals. The difference between the introduced dynamic modal control of the unmanned vehicle and the static one is formulated. Some fragments displaying 1D-signals in a wavelet medium are introduced into the autonomous and external control subsystems. The computer-aided control system uses such elements of the wavelet transforms technique as Gabor wavelet functions, the wavelet matching pursuit algorithm, and Cohen’s class time-frequency distributions. The research results in formulating the criteria for forming the unmanned vehicle current trajectories by the control system in the form of its reactions to sporadic disturbances caused by the occurrence of static or dynamic obstacles on a route. The algorithm of dynamic modal control of current trajectories has been developed. The concept of forward and reverse transient processes of signals of unmanned vehicle trajectory deviation has been introduced. The estimation procedure of modal controller parameters has been described. The algorithm has been developed for modal controller matrix recalculation, which has the form of the chain of sequentially implemented matrix procedures. It should be noted in conclusion that a computer-aided system for modal control of current trajectory deviation has been developed on the basis of the performed research. It enables to implement the functions of controlling the dynamics of technological and safe movement of unmanned vehicles along the quarry routes in a conflict environment of open pit mining.

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