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Algorithmic method for phase angle shift of noisy voltages using conditional averaging of delayed signal's absolute value

Kowalczyk A., Szlachta A.

Metrology and Measurement Systems

2011

Vol. 18, nr 1

137-144

The method of a phase shift angle measurement using conditional averaging of delayed signal absolute value (CAAV) is presented in this paper. The input sinusoidal signal x(t) is without noise. White noise with normal distribution and band limited to low frequencies has been applied as disturbance of delayed sinusoidal signal z(t). Noise n(t) - N(0, δn) is added to the delayed signal - the noised and delayed signal z(t) is obtained. The phase angle shift is proportional to time location of CAAV's minimum (minimum of the characteristic of conditional averaging of delayed signal's absolute value). The phase angle shift can be determined on the basis of conditional averaging value of elaborated algorithm. The characteristics of conditional average of delayed signal's absolute value in the surrounding of the minimum of this function (the results of practical investigations and theoretical calculation) are presented. The experimental variance of characteristic CAAV in surroundings of the minimum (obtained from practical investigations and calculation) is illustrated in the paper. The algorithms of conditional averaging have been elaborated and practically realized in the LabVIEW environment.