Gabor frames generated by random-periodic time-frequency shifts

Sarthak Raj

Session: General

Keywords: Gabor frames, random-periodic time-frequency shifts

TL;DR: Gabor frames generated by random-periodic time-frequency shifts

Abstract:

we consider a variation of the existence of
Gabor frames in a probabilistic setting, in which we consider
time-frequency shifts taken over random-periodic sets. We demonstrate
that the method of selecting random-periodic time-frequency shifts is
successful with high probability for specific categories of well-behaved
functions, notably including Hermite functions, totally positive
functions, and B-spline functions. In particular, we show that if $x_1,
x_2, \ldots ,x_m$ are independent and uniformly distributed in $[0,1),$
with $m$ sufficiently large, then the set of time-frequency shifts
$\Lambda \times \mathbb{Z}, $ where $\Lambda=\mathbb{Z} + \{x_1, x_2, \ldots, x_m\},$
forms Gabor frame with high probability.

Submission Number: 136