Some problems of discretization and determination of basic parameters of harmonic signals

The formulation and proof of the theorem on the necessity and sufficiency of three instantaneous readouts of harmonic signals for determining their basic parameters (the amplitude, the frequency and the phase shift) are presented. The developed analog-digital algorithms for determining basic parameters of harmonic signals by the minimum of instantaneous readouts in a time shorter than their period are described on the basis of the proved theorem. The results of mathematical modeling of the developed algorithm of determining the frequency of a harmonic signal by the probabilistic-statistical method are presented. Algorithm errors for determining the frequency of both a pure harmonic signal, and a signal with five harmonics with different accuracy of representation in amplitude of discrete values of signals are investigated.