Wavelets: A Positional Notation for Functions

Howard L. Resnikoff () and Raymond O. Wells ()
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Howard L. Resnikoff: Future WAVE Inc.
Raymond O. Wells: Rice University, Department of Mathematics

Chapter 3 in Wavelet Analysis, 1998, pp 30-36 from Springer

Abstract: Abstract Multiresolution representation is a new term for a very old idea. It describes what is also called a hierarchical structure. Hierarchical structures organize information into categories called levels and usually arrange it so that the higher in the hierarchy a level is, the fewer the number of members it has. Hierarchies are familiar in social and political organizations: A country has many states; a state has many counties; a county has many towns. The italicized words are names for levels in one way of organizing political subdivisions in a hierarchy. A hierarchical or multiresolution structure provides different ways of grouping things to reveal aspects of structure that depend on the scale of activity. Recalling the discussion of the previous chapter, we see that a multiresolution structure provides the necessary mechanism for extracting information from a sequence of measurements or calculations.

Keywords: Principal Part; Multiresolution Analysis; Music Notation; Residual Part; Positional Notation (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4612-0593-7_3

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