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

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.