Optimization of pulse width for frequency measurement by the method of rational approximations principle

Abstract

The purpose of any measurement is to obtain the required approximation to the measurand. In particular, when measuring time-frequency parameters, traditional methods require more time for measurement, if the frequency value has to be measured more accurately. It is proved that the principle of rational approximations is a method for estimating an unknown frequency, which is very precise, and requires a relatively short time for measurement. Its main properties are: (i) insensitivity to most known sources of uncertainty; (ii) the time required for the measurement is reduced when measuring higher frequencies; (iii) the accuracy of measurements depends on the stability of the reference frequency standard. The recently investigated property of the principle of rational approximations is the dependence of the measurement error on the width of the pulse in the signals used for measurement. In particular, if the pulse width is smaller, the error in the measurement process decreases more rapidly. However, a generally recognized model of analysing how short the pulse width should be is not yet created. In the present paper, a formalism has been developed to determine the optimum pulse width in order to minimize both the magnitude of the error and the measurement time. Variation of this parameter permits to obtain the best approximation to the measurand from the very first moments of measurement. The minimum time required for the measurement was thoroughly analysed.