OPERATIVE RECOGNITION OF STANDARD SIGNAL TYPES
DOI:
https://doi.org/10.15588/1607-3274-2020-2-8Keywords:
Disproportion functions, type of numerical function, sinusoid distortion, exponential function, polynomial function, power function.Abstract
Context. Recognizing the type of function regardless of its parameters is an urgent task.
Objective. To develop methods for the operational quantitative measurement of deviations of the type of the analyzed function, representing the analyzed process, from the standard types of functions: power, polynomial, exponential and sinusoidal according to the data obtained at the current time.
Method. To solve the problem, methods based on disproportion functions have been developed. The existing disproportion functions and their application for the recognition of power and polynomial functions are given. To recognize the exponential and sinusoidal functions at the current time, the disproportion over the first-order derivative with respect to its derivatives is used. With the parametric specification of functions, it is the difference between the ratios of the values of two functions and the ratio of their first derivatives for a given parameter value. In the case of a proportional relationship between two functions, this disproportion function is equal to zero for any value of the proportionality coefficient. It is shown that if for a given value of the argument the disproportion over the first-order derivative of the analyzed function with respect to its first derivative is zero, this is a sign that the function is exponential at this point regardless if it’s parameters. To control the sinusoidality at the current time, the disproportion over the first-order derivative of the analyzed function with respect to its second derivative is calculated. If it is zero, this is a sign that the function is sinusoidal at a given point regardless of its amplitude, frequency and phase of the oscillations. It is shown that in this way it is also possible to control the sum of sinusoids with different amplitudes and phases, but with the same frequency. You can also control second-degree sine waves.
Results. The effectiveness of the proposed methods is shown by computer simulation of the decay of radioactive isotopes, as well as simulation in violation of the sinusoidal nature of the controlled process.
Conclusions. Based on the disproportion functions, methods have been developed for the operative recognition of the type of function that describes the analyzed process. These methods can be used to analyze chemical-technological processes, control the purity of radioactive isotopes, and also to control the sinusoidality of processes in electrical networks.
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