A Signal-Dependent Evolution Kernel for Cohen Class Time–Frequency Distributions

1998 ◽  
Vol 8 (3) ◽  
pp. 158-165 ◽  
Author(s):  
N.Sudarshan Rao ◽  
P.S. Moharir
Keyword(s):  
Frequency Distributions ◽  
Time Frequency ◽  
Class Time ◽  
Evolution Kernel ◽  
Cohen 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

Pseudo Cohen Time-Frequency Distributions in Infinite Variance Noise Environment

2013 ◽  
Vol 475-476 ◽  
pp. 253-258
Author(s):  
Hai Bin Wang ◽  
Jun Bo Long ◽  
Dai Feng Zha
Keyword(s):  
Order Statistic ◽  
Stable Distribution ◽  
Impulsive Noise ◽  
Infinite Variance ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Noise Environment ◽  
Class Distribution ◽  
Cohen Class ◽  
Low Order

stable distribution has been suggested as a more appropriate model in impulsive noise environment.The performance of conventional time-frequency distributions (TFDs) degenerate in stable distribution noise environment. Hence, three improved methods are proposed based on Fractional Low Order statistics, Fractional Low Order Wigner-Ville Distribution (FLO-WVD), Fractional Low Order Statistic pseudo Wigner-Ville Distribution (FLO-PWVD), Fractional Low Order Statistic Cohen class distribution (FLO-Cohen). In order for real-time, on-line operation and fairly long signals processing, a new smoothed pseudo Fractional Low Order Cohen class distribution (PFLO-Cohen) is proposed.Simulations show that the methods demonstrate the advantages in this paper, are robust.

Enhanced Cohen class time–frequency methods based on a structure tensor analysis: Applications to ISAR processing

2013 ◽  
Vol 93 (7) ◽  
pp. 1813-1830 ◽  
Author(s):  
Vincent Corretja ◽  
Eric Grivel ◽  
Yannick Berthoumieu ◽  
Jean-Michel Quellec ◽  
Thierry Sfez ◽  
...  
Keyword(s):  
Structure Tensor ◽  
Tensor Analysis ◽  
Time Frequency ◽  
Class Time ◽  
Cohen 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.

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