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).