Signal Analysis Using Rough Integrals

Abstract

This paper presents an approach to the use of rough integrals in signal analysis. For each set of sample sensor signal values, the average accuracy of set approximation is computed using a rough integral. In rough set theory, set approximation is carried out in non-empty, finite universes of objects. In this article, by contrast, set approximation is carried out inside non-empty, uncountable sets (universes) of points. This study is motivated by an interest in classifying sample values for various types of sensors. One result of this study has been the introduction of discrete integrals based on rough set theory. The rough integrals used in this article have practical implications, since these integrals serve as an aid in sensor reduction and in pattern recognition in analyzing segments of continuous signals. In the context of sensor reduction, rough integrals provide a basis for determining the relevance of sensors over a particular sampling period. In the context of pattern recognition, rough integrals can be useful in doing such things as classifying radar weather data, vehicular traffic patterns, robot navigation and waveforms of power system faults. A sample application of the rough integral in estimating the accuracy of set approximation of a sensor signal is given. The contribution of this article is an approach to measuring the relevance and accuracy of approximation of sample sensor signal values based on rough set methods.