О ПОГРЕШНОСТИ КОРРЕЛЯЦИОННОГО МЕТОДА ИЗМЕРЕНИЙ, ИСПОЛЬЗУЮЩЕГО ПСЕВДОСЛУЧАЙНЫЕ СИГНАЛЫ
ON THE ERROR OF THE CORRELATION METHOD OF MEASUREMENT USING A PUSH-SUCCESSIVE SIGNALS
Сторінки: 137-141. Номер: №3, 2019 (273)
Автори:
А.А. ВИШЕНСКИЙ
Национально-технический университет Украины «Киевский политехнический институт им. И. Сикорского»
ALEKSANDR ALEKSANDROVITSH VISHENSKIY
National Technical University of Ukraine “I. Sikorsky Kyiv Polytechnic Institute”
DOI: https://www.doi.org/10.31891/2307-5732-2019-273-3-137-141
Рецензія/Peer review : 02.05.2019 р.
Надрукована/Printed : 02.06.2019 р.
Анотація мовою оригіналу
Корреляционный метод определения характеристик динамических систем является весьма важным методом анализа, который рассматривается в статье. В частности, решается задача оценки погрешностей, которые возникают при его использовании. Исследован погрешности, обусловленные не идеальностью характеристик при идентификации случайного процесса. Решение этой задачи заключается в получении необходимых требований к генератору шума. В итоге получено количественное соотношение для каждого конкретного случая, оценивающее погрешность определения импульсной характеристики исследуемой системы.
Ключевые слова: корреляционный метод, корреляционная функция, М-последовательности, дискретизация спектра, уравнение Винера-Хопфа, свертка
Розширена анотація англійською мовою
Correlation method for determining the characteristics of dynamic systems is a very important method of analysis, which is considered in the article. In particular, the problem of estimating the errors that arise when using the correlation method is solved. The investigated errors due to non-ideal characteristics when identifying a random process. The solution to this problem is to obtain the necessary requirements for the noise generator. The initial premise of the stated material is an imitation of a random process using pseudo-random numerical M-sequences. The solution to this problem is to obtain the necessary requirements for the noise generator. The initial premise of the stated material is an imitation of a random process using pseudo-random numerical M-sequences. The use of these sequences causes specific errors of two types, among which there is an error due to the periodic repetition of sections in them. The second error is caused by the presence of a correlation between the elements of the sequence, i.e. it is actually due to the finite transmission bandwidth of the process. At a qualitative level, based on a priori information about the possible values of the parameters of the estimated impulse response of the system, the conditions that the test sequence of random numbers must satisfy are determined. The first such condition, which is determined, is that the period of repetition of sections of a sequence is obviously a larger integral, on which the impulse response is nonzero. The second is that the test sequence has a uniform portion of the energy spectrum, the width of which exceeds the frequency band with frequency characteristics other than zero. These conditions obtained on the basis of the physical meaning of the correlation method are approximate. As a result, a quantitative ratio, for each specific case, was obtained, evaluating the error in determining the impulse response of the system under study. Based on this assessment, it is easy to determine the required characteristics of the test sequence for practical purposes.
Keywords: correlation method, correlation function, M-sequences, spectrum discretization, Wiener-Hopf equation, convolution.
References
- Granovskij V.A. Dinamicheskie izmereniya. Osnovy metrologicheskogo obespecheniya / V.A. Granovskij. – L. : Energoatomizdat, 1984. – 224 s.
- Soroko L.M. Osnovy golografii i kogerentnoj optiki / L.M. Soroko. – M. : «Nauka» Glavnaya redakciya fiziko-matematicheskoj literatury, 1971. – 616 s.
