Temporal granulation and its application to signal analysis

Abstract

In this study, we elaborate on the role of information granulation and the ensuing information granules in description of time series and signal analysis, in general. Information granules are entities of elements (quite commonly, numeric data) that are combined together (aggregated) owing to their vicinity, similarity and alike. Proceeding with a given window of granulation (that is an initial collection of numeric data), we propose an algorithm that produces a complete information granule – fuzzy set. The principle supported by the method leads to the formation of fuzzy sets that are legitimate in terms of experimental data being at the same time maximized with regard to their specificity (compactness). It has been shown that information granules can be are regarded as generic conceptual entities contributing to the description of numeric time series. In this capacity, they are used as building blocks aimed at achieving high level, compact, and comprehensible models of signals. More importantly, the phase of information granulation could be viewed as a prerequisite to more synthetic and abstract processing such as the one witnessed in syntactic pattern recognition