Formation of Discrete Signals on a Two-Sided Infinite Interval Using Recursive Models

To approximate discrete signals given on an infinite two-sided time interval, it is proposed to use a new approach based on the use of a two-component recursive model with a special right-hand side. The advantages of this approximation in comparison with other known ones are substantiated. A method is developed for optimal estimation of the parameters of the proposed recursive model from a finite set of signal samples in the time domain. On its basis, analytical expressions for the algorithm of the best approximation and subsequent recurrent formation of a discrete signal are obtained. Strict analytical expressions are obtained for the complex and amplitude spectra of the approximating signal. Experimental results are presented confirming the good quality of the proposed two-component recursive approximation of the signal both in the time and spectral domains.