A posteriori approach for estimating the signal-sampling interval on the basis of interpolation by bordering functions
Andrey Vladimirovich Sedov, Kirill Zharikov · Известия высших учебных заведений Электромеханика · 2024
The article considers the approach, estimating correctness of sampling frequency selection at measurement of physical processes from the point of view of distortions introduced by discrete signal representation. It does not require multiple repeated measurements of the signal with different uniform sampling intervals and the use of computationally complex spectral transformations. A single measurement of the signal with a fixed uniform sampling interval, as well as several control points at time instants that are not multiples of the selected frequency, is implemented. Application of the inter-polation formula with bordering functions allows estimating the values in the selected control points from the uniform signal samples. Based on the comparison of calculated and measured values in the control points, the conclusion about the quality of sampling frequency selection is made. The used interpolation does not require calculation of the coeffi-cients of the interpolating trigonometric polynomial or spectral characteristics, and the estimation is carried out ‘by nodes’, similar to the way it is realised in the interpolating Lagrangian polynomial. The approach reveals the presence of distortion both for the case where the observation interval is the period of the signal and for the case where it is not the period of the signal. The second case is more complicated, as in this case, due to the effect of spectrum spreading, there is additionally a distortion of the measured signal, which can be incorrectly attributed to the wrong choice of the sam-pling interval due to the failure to fulfil the condition of the sampling theorem. To identify this case, the article proposes using a special application of time windows to the occurring errors at the control points on the observation interval.