The Fast Interpolation Transformation and the Sampling Theorem on the Basis of Bordering Functions for Recording the Wave Signals of Mechanical and Other Physical Fields

The approach of the fast interpolation of discrete signals in multi-speed microprocessor systems for recording signals of wave and resonance changes in mechanical and other physical fields is considered. Interpolation is carried out on the basis of bordering functions that simplify and accelerate the process of signal restoration. A set of interconnected sampling theorems is formulated on the basis of bordering functions for cases of uniform and non-uniform sampling of signals. A certain hierarchy of these theorems and their interrelation with the well-known Kotelnikov-Shannon sampling theorem are established. New concepts of a quasi-orthogonal system of basis functions and a quasi-unit matrix are proposed.