Uncertainty principles for orthonormal sequences
By Philippe Jaming, Alexander M. Powell. 2006
51 citations recorded by the source corpus.
Abstract The aim of this paper is to provide complementary quantitative extensions of two results of H.S. Shapiro on the time–frequency concentration of orthonormal sequences in L 2 ( R ) . More precisely, Shapiro proved that if the elements of an orthonormal sequence and their Fourier transforms are all pointwise bounded by a fixed function in L 2 ( R ) then the sequence is finite. In a related result, Shapiro also proved that if the elements of an orthonormal sequence and their Fourier transforms have uniformly bounded means and dispersions then the sequence is finite. This paper gives quantitative bounds on the size of the finite orthonormal sequences in Shapiro's uncertainty principles. The bounds are obtained by using prolate spheroidal wave functions and combinatorial estimates on the number of elements in a spherical code. Extensions for Riesz bases and different measures of time–frequency concentration are also given.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing
View Paper: https://www.semanticscholar.org/paper/be43297d10323018fbbd3ad196ef7455f56673fc
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In Applied Mathematics
In Computer Vision and Pattern Recognition
In Signal Processing
Citations in the corpus
- Orthonormal Sequences in L2(Rd) and Time Frequency Localization (2009, methodology): “2 Inequalities for Orthonormal Sequences In this subsection we follow the ideas of [14], where various inequalities for orthonormal sequences were derived from a one-dimensional localization principles.”