МЕТОД ОЦІНЮВАННЯ ШУМІВ В БАГАТОКАНАЛЬНІЙ ВИМІРЮВАЛЬНІЙ ІНФОРМАЦІЙНІЙ СИСТЕМІ НА ОСНОВІ ДЕКОМПОЗИЦІЇ СИНГУЛЯРНИХ ЗНАЧЕНЬ МАТРИЦІ ДАНИХ
DOI:
https://doi.org/10.30837/2663-9564.2025.2.03Ключові слова:
багатоканальна вимірювальна інформаційна система, декомпозиція сингулярних значень, матриця експериментальних даних, фільтрація шумуАнотація
Фільтрація шумів широко впроваджена в теорії і техніці обробки сигналів. Значно менша кількість наукових робіт присвячена вилученню шумів з реалізацій випадкових процесів з метою їх аналізу для специфічних завдань. У статті запропоновано метод розділення сигналів і шумів у багатоканальній вимірювальній інформаційній системі. Для цього використовується матриця експериментальних даних і за допомогою декомпозиції сингулярних значень (singularvaluedecomposition – SVD) здійснюється аналіз сингулярних мод цієї матриці та парціальних матриць, які є складовими матриці даних. Визначені умови, при яких парціальна матриця першого порядку буде описувати сигнали в каналах системи, а матриці вищих порядків містять шумові компоненти. Для цього косинус кута між матрицею даних та першою парціальною матрицею повинен наближатися до одиниці, а між матрицею даних та другою матрицею – до нуля. Такі умови досягаються у випадках перевищення порогового рівня відношенням сигнал/шум. Отримані шуми в окремих випадках можуть використовуватися для визначення похибок вимірювання.
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