Examining signal estimation methods by including missing signal parts

抄録

A signal often includes missing parts and is often affected by noise when it is obtained; thus, all available data includes errors. In this study, we considered a method in which only highly reliable signals, which are close to the true value, are extracted for estimating the signals. When highly reliable signals (candidate points) are extracted from the acquired signals at an arbitrary ratio, the signals from the remaining parts constitute the missing parts. The signals with missing parts after the extraction of the candidate points were estimated by Fourier series approximation. Herein, we examined the optimal extraction ratio for the estimation, including the order used for approximation. First, we examined the required percentage of the candidate points extracted from the acquired signals for increasing the estimation accuracy. As a result, if at least about 80% candidate points are available, the estimation accuracy was high. Subsequently, we proposed three methods for selecting the candidate points; we compared the errors between the original and the estimated signals, and the estimation iteration times. Consequently, the following method had the highest estimation accuracy. Further, we performed the estimation once using all the obtained signals and then removed the signal with large error between the original and the estimated signals at an arbitrary ratio and performed the estimation again. In this method, we can extract signals close to the true value. This method has fewer iteration times compared with other methods. Furthermore, by using the third order, the error was insignificant and the number of calculations was also limited.