Colloquium
3:00 p.m., Friday (January 16th)
Math Annex 1100
Ozgur Yilmaz
University of Maryland, College Park
Approximation Theory of Quantization of Redundant Expansions
A basic problem in signal processing, when analyzing a given signal
of interest, is to obtain a digital representation that is suitable
for storage, transmission, and recovery. A reasonable approach is
to first decompose the signal as a sum of appropriate harmonics,
where each harmonic has a real (or complex) coefficient. Next,
one "quantizes" the coefficients, i.e., one replaces each
coefficient by an element of a given finite set (e.g., {1,1}).
The problem of how to quantize a given expansion is nontrivial
when the expansion is redundant.
In this talk, we consider (redundant) frame expansions, and show
that SigmaDelta modulators provide efficient quantization
algorithms in the cases of oversampled bandlimited functions,
Gabor frame expansions of squareintegrable functions, and
finite frame expansions in Euclidean space. In particular,
we show that SigmaDelta algorithms outperform PCM algorithms
(the current stateoftheart). We also address the problem
of optimal quantization, and present recent results in the case
of finite frames.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
