Stability results for Gabor frames and the p-order hold models

TL;DR

This paper establishes stability results for Gabor frames with specific window functions, providing insights into how timing jitters affect signal reconstruction in p-order hold models.

Contribution

It introduces new stability results for Gabor frames with Sobolev and B-spline windows, linking them to timing jitter effects in p-order hold signal reconstruction.

Findings

Stability results for Gabor frames with Sobolev and B-spline windows.

Application of results to analyze timing jitters in p-order hold models.

Enhanced understanding of signal reconstruction robustness.

Abstract

We prove stability results for a class of Gabor frames in $ L^2(\R)$. We consider window functions in the Sobolev spaces $H^1_0(\R)$ and B-splines of order $p\ge 1$. Our results can be used to describe the effect of the timing jitters in the $p$-order hold models of signal reconstruction.