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

机译：通过理性近似方法的频率测量优化脉冲宽度原理

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摘要

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.
机译：任何测量的目的是获得对测量的所需近似。特别地，如果测量时间频率参数，传统方法需要更多时间测量，如果必须更准确地测量频率值。事实证明，理性近似的原理是估计未知频率的方法，这非常精确，并且需要相对较短的测量时间。其主要属性是：（i）对大多数已知的不确定性来源的不敏感; （ii）测量频率较高时测量所需的时间; （iii）测量的准确性取决于参考频率标准的稳定性。理性近似原则的最近调查的属性是测量误差对用于测量的信号中脉冲宽度的依赖性。特别地，如果脉冲宽度较小，则测量过程中的误差更快地减小。但是，尚认尚未创建脉冲宽度的分析模型。在本文中，已经开发了一种形式的形式，以确定最佳脉冲宽度，以便最小化误差的大小和测量时间。该参数的变化允许从第一矩的测量时刻获得对测量的最佳近似。彻底分析了测量所需的最短时间。

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