This paper presents a new method for reconstruction of trigonometric polynomials, a specific class of bandlimited signals, from a number of integrated values of input signals. It is applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The proposed method of processing can be used for precise rms measurements of periodic signal (or power and energy) based on the presented signal reconstruction. Based on the value of the integral of the original input (analogue) signal, with a known frequency spectrum but unknown amplitudes and phases, a reconstruction of its basic parameters is done by the means of derived analytical and summarized expressions. Subsequent calculation of all relevant indicators related to the monitoring and processing of ac voltage and current signals is provided in this manner. Computer simulation demonstrating the precision of these algorithms. We investigate the errors related to the signal reconstruction, and provide an error bound around the reconstructed time domain waveform.

Synchronous sampling allows alternating current (AC) quantities, such as the root mean square (RMS) values of voltage and power, to be determined with very low uncertainties (on the order of a few parts of 10-6 [1]). In this paper, a mathematical expression for estimating measurement uncertainties in nonideal synchronization with fundamental frequency AC signals is presented. The obtained results were compared with those obtained by measurements with a high-precision instrument used for measuring basic AC values.