相关论文: Approximation of dual Gabor frames, window decay, …

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…

We investigate vector-valued Gabor frames (sometimes called Gabor superframes) based on Hermite functions $H_n$. Let $h= (H_0, H_1, ..., H_n)$ be the vector of the first $n+1$ Hermite functions. We give a complete characterization of all…

We apply the orthonormalization procedure previously introduced by two of us and adopted in connection with coherent states to Gabor frames and other examples. For instance, for Gabor frames we show how to construct $g(x)\in L^2(\Bbb{R})$…

Numerous linear and non-linear data-detection and precoding algorithms for wideband massive multi-user (MU) multiple-input multiple-output (MIMO) wireless systems that rely on orthogonal frequency-division multiplexing (OFDM) or…

In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will…

The quantum mechanical harmonic oscillator Hamiltonian generates a one-parameter unitary group W(\theta) in L^2(R) which rotates the time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When W(\theta) is applied to any…

In this article we are going to discuss the conjecture of Strohmer and Beaver for Gaussian Gabor systems. It asks for an optimal sampling pattern in the time-frequency plane, where optimality is measured in terms of the condition number of…

We consider Gabor frames generated by a general lattice and a window function that belongs to one of the following spaces: the Sobolev space $V_1 = H^1(\mathbb R^d)$, the weighted $L^2$-space $V_2 = L_{1 + |x|}^2(\mathbb R^d)$, and the…

Gabor frames play a vital role not only modern harmonic analysis but also in several fields of applied mathematics, for instances, detection of chirps, or image processing. In this work we present a non-trivial generalization of Gabor…

In this work we study families of pairs of window functions and lattices which lead to Gabor frames which all possess the same frame bounds. To be more precise, for every generalized Gaussian $g$, we will construct an uncountable family of…

This paper investigates the optimization of dual frame pairs in the context of erasure problems in data transmission, using a graph theoretical approach. Frames are essential for mitigating errors and signal loss due to their redundancy…

In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…

We derive frame estimates for vector-valued Gabor systems with window functions belonging to Schwartz space. The main result provides frame bound estimates for windows composed of Hermite functions. The proof is based on a recently…

Using Gabor analysis, we give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions, displaying a "Nyquist rate" which increases with $n$, the degree of polyanaliticity…

In this paper, we focus on constant-modulus waveform design for the dual use of radar target detection and cellular transmission. As the MIMO radar typically transmits orthogonal waveforms to search potential targets, we aim at jointly…

We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in…

Quantum phase estimation is an important component in diverse quantum algorithms. However, it suffers from spectral leakage, when the reciprocal of the record length is not an integer multiple of the unknown phase, which incurs an accuracy…

We develop an alternative approach to the study of Fourier series, based on the Short-Time-Fourier Transform (STFT) acting on $L_{\nu }^{2}(0,1)$, the space of measurable functions $f$ in ${R}$, square-integrable in $ (0,1)$, and…

We study an intriguing question in frame theory we call "Weaving Frames" that is partially motivated by preprocessing of Gabor frames. Two frames $\{\varphi_i\}_{i\in I}$ and $\{\psi_i \}_{i\in I}$ for a Hilbert space ${\mathbb H}$ are…

Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…