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Постановка и решение основной задачи линейной оптимальной фильтрации

Постановка и решение основной задачи линейной оптимальной фильтрации

Abstract

In the work interpretation of time sequences from the viewpoint of dynamic modeling has been considered. The developed technique can be used for the decision of rather wide range of problems, namely: at designing linear optimum filters; separation (division) of mix of signals on components; research of dynamic parameters of time numbers; the frequency analysis and others. In particular, by working out linear optimum filters on a signal unique restriction invariance in time of its statistician of the second order has been imposed. It can be noticed that the classical approach at the decision of this problem imposes on an investigated signal essential aprioristic restrictions which are actually carried out only for a very narrow class of data.

Рассматривается интерпретация временных последовательностей с точки зрения динамического моделирования. Разработанная методика может использоваться для решения достаточно широкого круга задач, а именно: при конструировании линейных оптимальных фильтров; сепарации (разделении) смеси сигналов на компоненты; исследовании динамических параметров временных рядов; частотном анализе и других. В частности, при разработке линейных оптимальных фильтров на сигнал накладывается единственное ограничение инвариантность во времени его статистик второго порядка. Отметим, что классический подход при решении этой задачи накладывает на исследуемый сигнал существенные априорные ограничения, которые фактически выполняются только для очень узкого класса данных.

Keywords

ОПТИМАЛЬНЫЕ ЛИНЕЙНЫЕ ФИЛЬТРЫ, БЕЛЫЙ ШУМ, ЦВЕТНОЙ ШУМ, ФУНКЦИЯ АВТОКОРРЕЛЯЦИИ, ФУНКЦИЯ ВЗАИМНОЙ КОРРЕЛЯЦИИ, ИНТЕГРАЛ СВЕРТКИ, ФИЛЬТР КОЛМОГОРОВА-ВИНЕРА, СЕПАРАЦИЯ СИГНАЛОВ, ДИНАМИЧЕСКИЕ ПАРАМЕТРЫ, KOLMOGOROV-WIENER'S FILTER

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
gold