Z-Transform Exponential Approximation of One-Dimensional Functions: Theory and Applications

A new method of interpolation/approximation of univariate functions using exponential polynomials, both complete and reduced, generally using complex polynomials, was suggested. The solution is based on the Z-transformation of one variable function, predetermined by a discrete set of equally spaced samples. For the first time, the problem was solved for dynamic systems with proper frequencies of any multiplicity. The method of transition from time functions to full, and shortened operator models of selective radioelectronic devices was represented. In addition, the transfer ratio, reduced by Z-transform, corresponds exactly to the basic approximation in the modified method of the truncated operator equations. Based on some examples including IFA of ninth order (with three poles, each of which having multiplicity factor three) on exposure to complex FM/PM input signal, the usage possibility of precise as well as shortened exponential and operator polynomials aimed to design radioelectronic systems which are sensitive to phase variation during the transition process, was proved.