Triangular window weighted algorithm for RMS value measurement

After analyzing the direct sampling algorithm for measuring a periodic signal's RMS value, a triangular window weighted algorithm is proposed for effectively reducing the synchronous error. Analytic formulas of measured RMS value as a function of the relative frequency deviation and initial sampling phase (or time) is derived. Both theory and numerical simulations show that the measurement error of the RMS value is proportional to the relative frequency deviation using the direct sampling algorithm, while it is proportional to the square of the relative frequency deviation using the proposed algorithm. Furthermore, the proposed algorithm is quite suitable for on-line implementation and the measured value responds rapidly to signal's variation. If the frequency deviation is far less than one, very high accurate measuring results can be achieved even if no synchronous sampling technique is introduced.