Recovery of Discrete-Time Signal Based on the Moving Average Model and Estimation of the Samples Correlation in Forward and Reverse Forecasting

Abstract

The article discusses the development of mathematical support for the recovery of the values of discrete-time sequence samples obtained as a result of uniform sampling of a continuous signal. The recovery problem of discrete-time sequence samples is solved for a signal that can be considered stationary or stationary at least in a broad sense (quasi-stationary). The development of mathematical support for the recovery of the values of signal samples was carried out on the basis of constructing a moving average model and estimating the correlation of signal samples over time with forward and reverse forecasting. Estimates of the signal correlation function necessary to recover sample sections with lost values are calculated from samples with known values. Correlation function estimates can be calculated regardless of the location of the recovery area when the condition of stationarity of the signal is met. The obtained estimates of the correlation function samples can be used for both forward and reverse forecasting. Moreover, even if it is necessary to recover several problem sections, it is enough to calculate only once the sample of correlation function estimates necessary for their restoration. The resulting mathematical solution to the problem became the basis for the development of algorithmic support. Test tests and functional checks of the algorithmic support were carried out on the basis of simulation using a signal model representing an additive sum of harmonic components with random initial phases. The simulation results showed that the calculation of estimates of the lost sample values is carried out with a fairly low error, both in forward and reverse forecasting, as well as when they are used together. In practice, the choice of a sequence recovery algorithm based on forward or reverse forecasting will be determined based on the actual conditions of its processing. In particular, if previous samples with known values are not enough to carry out forward forecasting, then the reverse forecasting procedure is implemented and vice versa. The developed algorithmic support can be implemented in the form of metrologically significant software for digital signal processing systems.