Зображення широкосмугових взаємних функцій двох змінних у малохвильовій (вейвлет) області

• Date: 2023
• Main Authors: Наконечний, Адріан, Мусій, Роман, Наконечний, Ростислав
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2023
• Subjects: швидке перетворення Фур’є; неперервне вейвлет перетворення; дискретне вейвлет перетворення; вузькосмугова взаємна функція двох змінних; широкосмугова взаємна функція двох змінних.
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/253
• Journal Title: Physico-mathematical modeling and informational technologies

The main requirements for broadband signals are formulated. It is noted that the properties of the resolution of the wavelet transformation remain constant when the signals change over many octaves and make it possible to implement signal processing in a wide frequency range. It is shown that the broadband reciprocal function of two variables (BBRFTV) can be considered, if the appropriate mathematical requirements are met, as a valid small-wavelength transform that represents the similarity between one signal and many possible modified versions of another signal. The analysis of the BBRFTV was carried out depending on the order of mastabulation and displacement operations. For the analysis of broadband systems, it is proposed to use mutual BBRFTVs, which allow to obtain effective processing of the functions of two variables and at the same time better display the characteristics of signals for their further recognition and research. It has been established that since individual small-wave transformations take into account the non-stationary short-term (transient) characteristics of signals, in the case of the use of mutual BBRFTVs, there is a possibility of their application for the evaluation of spatial non-stationary systems.