During the last several years, frames have become increasingly popular; they have
appeared in a large number of applications, and several concrete constructions of frames of …

This is a survey about the theory of Gabor frames. We review the structural results about
Gabor frames over a lattice and then discuss the few known results about the fine structure …

We develop sub-Nyquist sampling systems for analog signals comprised of several, possibly
overlap**, finite duration pulses with unknown shapes and time positions. Efficient …

Let g∈ L2 (R) be a compactly supported function, whose integer-translates [Formula: see
text] form a partition of unity. We prove that for certain translation and modulation …

In this paper, we introduce the concept of periodic Gabor frames on non-Archimedean fields
of positive characteristic. We first establish a necessary and sufficient condition for a periodic …

We consider a general method for constructing dual Gabor elements different from the
canonical dual. Our approach is based on combining two Gabor frames such that the …

Gabor analysis is a method for analyzing signals through the use of a set of basic building
blocks. The building blocks consists of a certain function (the window) that is shifted in time …

Many practical machine learning tasks employ very deep convolutional neural networks.
Such large depths pose formidable computational challenges in training and operating the …

We study totally positive (TP) functions of finite type and exponential B-splines as window
functions for Gabor frames. We establish the connection of the Zak transform of these two …

Consider a bounded function g supported on [− 1, 1] and a modulation parameter b∈] 1/2, 1
[for which the Gabor system [Formula: see text] is a frame. We show that such a frame …