Mathematical Recovery of Measurement Signals using Test Trials of Processing Systems

Mathematical methods for the recovery of the signals distorted and noisy during their measurements by linear stationary systems using test trials of these systems are considered. Instead of hardware functions, usually belonging to the class of generalized ones, test signals from the class of main functions are used, which makes it possible to carry out non-blind reconstruction of signals without determining their distortion functions and to use regularization techniques to reconstruct real nondeterministic signals with noise and uncertainties. Signal recovery using test methods can improve the quality of measurements by several orders of magnitude without complex and expensive hardware modifications. Numerical experiments on signal reconstruction at various noise levels are presented.