Accurate RMS calculations for periodic signals by Trapezoidal rule with the least data amount

Abstract

The purpose of this research is to present a simple method using the least data amount to calculate root mean square (RMS) values of periodic signals (constructed from Fourier series) which the highest harmonic order is known or able to be estimated. In the research, trapezoidal rule with the least data amount was proved and tried to calculate definite integral values of sinusoidal signals from a lot of trial runs until a significant property was found. Then the property would be deployed to calculate RMS values. Results of the research can provide not only more convenient processes of simple trapezoidal rule but also more accurate results than the patented Simpson's rule in the same least data amount. © 2013 Sompop Poomjan et al.