Algorithmic Approach to Selecting Digital Filtering Methods for Processing Dynamic Measurement Results

The restoration of dynamically distorted signals over short time intervals represents a complex inverse problem in dynamic measurements. In the presence of various types of noise, the output signal becomes corrupted, further complicating the task. To date, the theory of optimal dynamic measurements has been developed, employing methods from optimal control theory, Sobolev-type equations, and stochastic differential equations, alongside advanced numerical techniques. Previously, the authors conducted multiple studies advancing numerical methods for retrieving the input signal as a solution to the optimal control problem of dynamic measurement and proposed a new numerical algorithm for its resolution. When noise is present in the output signal, it is crucial not only to ensure the efficiency of the signal recovery algorithm, considering the measuring device’s inertia, but also to select the most effective digital filter. This article presents an algorithm within a software tool that facilitates the selection of one of three filters: a moving average filter, the Savitzky—Golay filter (based on the least squares method) followed by the optimal dynamic measurement algorithm, and the MSA method (an author-developed technique based on spline methods followed by averaging). The MSA method is not merely a digital filter; it integrates comprehensive noise filtering with an algorithm for optimal dynamic measurement. Moreover, it can be applied both in the presence and absence of noise and other disturbances. The novelty of these results lies in a systematic and comprehensive evaluation of the effectiveness and applicability of noise filtering methods for restoring dynamically distorted signals. This article provides the necessary theoretical background, general algorithmic schemes, experimental data, and results demonstrating the performance of the proposed approaches.