Kathi Selig
Trigonometric Wavelets and the Uncertainty Principle
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
41A10 Approximation by polynomials, {For approximation by trigonometric polynomials, See 42A10}
42A10 Trigonometric approximation
Abstract: The time-frequency localization of trigonometric wavelets is discussed.
A good measure is provided by a periodic version of the Heisenberg
uncertainty principle. We consider multiresolution analyses generated
by de la Vallee Poussin means of the Dirichlet kernel. For the
resulting interpolatory and orthonormal scaling functions and wavelets,
the uncertainty product can be bounded from above by a constant.
Keywords: periodic wavelets, time-frequency-analysis, uncertainty principle