Smooth PONS |
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Authors: | J S Byrnes W Moran B Saffari |
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Institution: | (1) Prometheus Inc., 21 Arnold Ave., 02840 Newport, RI;(2) University of Massachusetts at Boston, Boston, USA;(3) The Flinders University of South Australia, Australia;(4) University of Paris, Orsay |
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Abstract: | PONStm is a basis which satisfies all of the fundamental properties of the Walsh functions (each element is piecewise constant,
takes on only the values ±1, and can be efficiently computed via a fast transform) plus three additional properties that are
false for the Walsh functions: PONS is optimal with respect to a global uncertainty principle; all PONS elements have uniformly
bounded crest factors; and all PONS elements are QMF’s. In 1991, Ingrid Daubechies asked whether there exists a smooth basis
satisfying the global uncertainty principle property. In this article we show how to transform any basis into another basis
by applying the PONS construction, thereby providing an affirmative answer to this question. |
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Keywords: | primary 42A65 secondary 41A30 41A58 |
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