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Mathematics of Computation

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Recovering signals from inner products involving prolate spheroidals in the presence of jitter

Author: Dorota Dabrowska
Journal: Math. Comp. 74 (2005), 279-290
MSC (2000): Primary 68Q17, 94A12, 94A11; Secondary 94A20, 65G99
Published electronically: April 16, 2004
MathSciNet review: 2085411
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Abstract: The paper deals with recovering band- and energy-limited signals from a finite set of perturbed inner products involving the prolate spheroidal wavefunctions. The measurement noise (bounded by $\delta$) and jitter meant as perturbation of the ends of the integration interval (bounded by $\gamma$) are considered. The upper and lower bounds on the radius of information are established. We show how the error of the best algorithms depends on $\gamma$ and $\delta$. We prove that jitter causes error of order $\Omega^{\frac{3}{2}}\gamma$, where $[-\Omega,\Omega]$ is a bandwidth, which is similar to the error caused by jitter in the case of recovering signals from samples.

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Additional Information

Dorota Dabrowska
Affiliation: Faculty of Mathematics and Science, Cardinal Stefan Wyszyński University in Warsaw, ul. Dewajtis 5, 01-815 Warsaw, Poland

Keywords: Problem complexity, signal theory, application of orthogonal functions in communication
Received by editor(s): July 19, 2002
Received by editor(s) in revised form: June 2, 2003
Published electronically: April 16, 2004
Article copyright: © Copyright 2004 American Mathematical Society