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

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**74**(2005), 279-290 Request permission

## 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.## References

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## Additional Information

**Dorota Da̧browska**- Affiliation: Faculty of Mathematics and Science, Cardinal Stefan Wyszyński University in Warsaw, ul. Dewajtis 5, 01-815 Warsaw, Poland
- Email: dabrowska@uksw.edu.pl
- Received by editor(s): July 19, 2002
- Received by editor(s) in revised form: June 2, 2003
- Published electronically: April 16, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Math. Comp.
**74**(2005), 279-290 - MSC (2000): Primary 68Q17, 94A12, 94A11; Secondary 94A20, 65G99
- DOI: https://doi.org/10.1090/S0025-5718-04-01648-5
- MathSciNet review: 2085411