Primary Signal Processing and Algorithm for Selecting an Approximating Function in the Presence of a Noise Component

The article proposes an algorithm and mathematical for choosing the degree of polynomial approximation of a noisy signal in order to isolate its useful component.The proposed algorithm implements a two-level analysis of a digital signal.At the first stage, the signal is divided into components.To determine the points of sharp changes in the signal shape, a multicriteria filtering method.Its use allows us to isolate a low component function, determine function outliers, and also detect areas of sharp inflection of the function.Next, a polynomial approximation of the input sequence is applied, limited by the sections specified at the first stage of the algorithm.The paper presents a rationale for choosing depending data on the approximation type of the input component and determining the points of sharp change.For example, use line of an image obtained in the IR range to demonstrate the operation of the algorithm.The algorithm is used to detect the boundaries of objects on image.