Periodic non-harmonic signal effective value measurement in the presence of random noise using the approximation method

The paper describes an approximation method for determining the effective value of a periodic non-harmonic signal in the presence of random noise. To solve the problem for quickly result obtaining, signal processing is used for only half of its period. The proposed method is based on a parabolic spline approximation of discrete signal values. The error of the signal discrete values spline approximation is determined, as well as the error in the presence of random noise with a uniform distribution law. The analysis of the error of effective value determination by the considered method caused by the presence of random additive noise is presented. It is shown that the use of the spline function reduces the approximation error caused by random noise. The characteristics of the method considered are studied, as well the effective values of currents and voltages of the industrial power electrical equipment are determined. The use of the proposed method in determining the effective value of a non-harmonic periodic signal with the presence of a third harmonic is considered. It is proposed to use the considered approximation method for measuring the effective value of voltage and current of powerful electrical equipment in order to quickly determine its emergency situations.