Method for phase shift measurement using farey fractions

Abstract

The phase shift of coherent signals and the time intervals can be measured with the method of coincidences of electrical pulses. The results are automatically obtained and represented like simple fractions. These fractions are rational approximations of the unknown parameter, which generally is an irrational number. Such approximations can be represented with continued fractions or Farey fractions. Definitions and properties of Farey fractions are presented. An original method for phase shift measurement based on the pulses coincidence principle, whose result is a Farey fraction, is described. In order to increase the measurement accuracy, the continuous formation of rational means is performed, to represent the measurement result. These simplify the data processing and provide more accurate results than traditional methods.