Selection of error measure for discrete periodic signals at high levels of fluctuating noise

Abstract

The article covers the selection of an error measure for the results of Altering discrete noisy periodic signals when searching for optimal parameter values of the digital low-pass filter represented by the simple moving average. The following error measures were selected for comparison — Mean Square Error, Root Mean Square Error, Mean Absolute Error. To perform the experiments, a program generation of sinusoidal, triangular, square and sawtooth periodic waveforms was implemented. A series of experiments was carried out for generation and filtering of the noisy periodic signals with different noise levels. Values of error measures were found for filtered signals with different values of the digital filter parameter. Experimentally shown that at high noise levels the local minima of the objective functions are gradually transformed into straight lines and then into a monotonically increasing ones. Using the kurtosis measure the error measure was selected based on comparison results, representing the high-discernibility of local optima of the objective function at high levels of fluctuating noise.