The answer is provided by multiresolution analysis (MRA). It provides a simple hiearchical framework for identifying the properties of a signal, i.e. for taking note of its existence, for measuring it, for representing it, and for even reproducing it. A key aspect of this framework is its Hierarchical structure.
At different resolutions the details of a signal generally characterize different physical aspects of an event. At coarse resolution these details correspond to the larger overall aspects, the context of an event. At fine resolution these details correspond to its distinguishing features. Such a course-to-fine strategy is typical in identifying an event.
The mathematical formulation of this resolution hiearchy is developed in four steps.