A two-phase method of forming a granular representation of signals

This study focuses on a granular representation of signals. The development process dwells upon the use of the principle of justifiable granularity encountered in Granular Computing and the least square error method. This process consists of two phases where the construction of granular representatives of a family of signals (temporal data) is realized by invoking the design at the local and global level. At the local design level involving individual elements of the universe of discourse (time moments), the principle of justifiable granularity is applied to construct (a vertical part) information granules. At the global level, the least square error method is invoked to develop the bounds (envelopes) of the information granules already formed at the local level. Experimental studies are reported for the granular representation of synthetic data and publicly available ECG signals. Furthermore we demonstrate that the proposed approach can be used to construct fuzzy sets of type-2.