Minimization of Error in Distance Measurement in Industrial-Grade Frequency Range Finders with Weighted Averaging of Difference Frequency

Abstract

Analytic relationships for the errors in measurements of the frequency of a harmonic signal of limited length against a noise background with the use of the weighted method of frequency averaging are presented. Two parameters that provide an objective description of the properties of weighting functions in problems involved in the measurement of the frequency of a signal against a noise background are proposed. Optimality criteria of the weighting functions are formulated and a method of minimization of the measurement error is proposed.