Sigma-Delta Quantization and Finite Frames
John J. Benedetto
Director, Norbert Wiener Center; and University of Maryland, Department of Mathematics
Wednesday, November 2, 2005 15:00-16:00,
The theory of Sigma-Delta quantization is developed for finite frames for Euclidean space.
This theory, including the role of finite frames, is motivated by several recent applications in communications theory and code design.
Because of these applications, first order Sigma-Delta quantization schemes are constructed; and optimal quantization searches are designed.
Error estimates for various quantized frame expansions are derived, and, in particular,
it is shown that first order Sigma-Delta quantizers outperform the standard pulse code modulation (PCM) schemes using linear reconstruction.
The error estimates are comparable when consistent reconstruction methods are used in conjunction with PCM.
Higher order Sigma-Delta error estimates improve on the first order case.
Refined estimates in the first order case require the Erdos-Turan and Koksma number theoretic inequalities.
Further, the technology requires harmonic analysis, dynamical systems techniques, uniform distribution discrepancy theory,
and some methods from algebraic number theory.
Higher order schemes also involve tiling methods.
The theory is a collaboration with Alex Powell and Ozgur Yilmaz.
NIST North (820), Room 145
Wednesday, November 2, 2005 13:00-14:00,
John Benedetto received his PhD in 1964 from the University of Toronto under the direction of Chandler Davis,
who in turn studied under the famed algebraist, Garrett Birkhoff.
Professor Benedetto is Executive Editor and founding Editor-in-Chief of the Journal of Fourier Analysis and Applications,
and he is the Series Editor of Birkhauser's Applied and Numerical Harmonic Analysis book series.
He is a Distinguished Scholar-Teacher at the University of Maryland, and has been the PhD thesis adviser for 40 students.
Presentation Slides: PDF
Contact: P. M. Ketcham
Note: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.