Minimax Approximation of Representation Coefficients
from Generalized Samples
T. G. Dvorkind, H. Kirshner, Y.C. Eldar and M. Porat,
Department of Electrical Engineering,
Technion - Israel Institute of Technology
Haifa 32000, Israel
Abstract
Many sources of information are of analogue or continuous-time
nature. However, digital signal processing applications rely on
discrete data. We consider the problem of approximating L2 inner
products, i.e., representa-tion coefficients of a continuous-time
signal, from its generalized samples. Taking a robust approach,
we process these generalized samples in a minimax optimal sense.
Specifically, for the worst possible signal, we find the best
approximation of the desired representation coefficients by proper
processing the given sample sequence. We then extend our results
to criteria which incorporate smoothness constraints on the
unknown function. Finally we compare our methods with the
piecewise-constant approximation technique, commonly used for
this problem, and discuss the possible improvements by the
suggested schemes.
IEEE Trans. on Signal Processing,
Volume 55, Issue 9, pp. 4430 - 4443 (2007).

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