Using conditional averaging of delayed signals to measure phase shift angle

Abstract

Anovelmeasurementmethodandabriefdiscussionofbasiccharacteristicsofmeasuringthephaseshiftanglebetweentwosinusoidalsignalsofthesamefrequencyarepresentedinthispaper.Itcontainsamathematical modelforusingconditionalaveragingofadelayedsignalinterferedwithnoisetomeasurethephase shiftangle.Italsoprovidescharacteristicsofconditionalmeanvaluesanddiscussestheeffectofrandom interferencesontheaccuracyofthephaseshiftmeasurement.Thewaytodeterminethevarianceofthe conditionalmeanvalue,togetherwiththeassessmentofstandardandexpandeduncertainty,aredescribed. Theuncertaintycharacteristicshowsthecomplementarypropertiesofthediscussedanglemeasurement principle 𝜑 for small absolute values | 𝜑 | (minimum for 𝜑 = 0) relative to the correlation principle, where the minimum measurement uncertainty is present for 𝜑 = 𝜋 / 2.