This paper presents an overview of algorithms for one-phase active power estimation using digital signal processing in the time domain and in the frequency domain, and compares the properties of these algorithms for a sinusoidal test signal. The comparison involves not only algorithms that have already been published, but also a new algorithm. Additional information concerning some known algorithms is also included. We present the results of computer simulations in MATLAB and measurement results gained by means of computer plug-in boards, both multiplexed and using simultaneous signal sampling. The use of new cosine windows with a recently published iterative algorithm is also included, and the influence of additive noise in the test signal is evaluated.

This paper presents a universal approximation of the unit circle by a polygon that can be used in signal processing algorithms. Optimal choice of the values of three parameters of this approximation allows one to obtain a high accuracy of approximation. The approximation described in the paper has a universal character and can be used in many signal processing algorithms, such as DFT, that use the mathematical form of the unit circle. One of the applications of the described approximation is the DFT linear interpolation method (LIDFT). Applying the results of the presented paper to improve the LIDFT method allows one to significantly decrease the errors in estimating the amplitudes and frequencies of multifrequency signal components. The paper presents the derived formulas, an analysis of the approximation accuracy and the region of best values for the approximation parameters.