Processing of signals in linear systems - Evgeny Georgievich Zhilyakov; Sergey Pavlovich Belov; Tatyana Sergeevna Romankova; Ivan Ivanovich Oleinik (Наука. Инновации. Технологии, 2022)
Recovering signals is usually called compensation of distortions that occur when they are registered. The main problem studied in the literature is the instability of the calculated estimates of the input effects to the effects of errors in the registration of responses. Therefore, various methods of regularizing the initial equations are developed on the basis of their transformation into another equation, the solution of which is calculated stably. The most famous technique is the Tikhonov A.N. method of regularization. At the same time, in this paper it is shown that some of the information on the input action may be missing in the response, that is, even if there are no measurement errors, the resulting solution will be approximate. A method for estimating non-recoverable distortions caused by the operator of the recording system is proposed, which can be used at the stage of its synthesis. A linear form of the representation of the impact component accessible for restoration through the impulse response is obtained, so that the restoration problem is reduced to the calculation of its coefficients. A method for regularizing the systems of linear algebraic equations arising on this basis is proposed on the basis of adaptive estimation of the error levels of registration directly from the registered response.