Related papers: On Weaving Generalized Frames and Generalized Ries…
A geometric perspective involving Grammian and frame operators is used to derive the entire family of Welch bounds. This perspective unifies a number of observations that have been made regarding tightness of the bounds and their…
Given an orthonormal basis $ {\mathcal V}= \{v_j\} _{j\in N}$ in a separable Hilbert space $H$ and a set of unit vectors $ {\mathcal B}=\{w_j\}_{j\in N}$, we consider the sets $ {\mathcal B}_N$ obtained by replacing the vectors $v_1, ...,\,…
Integrating AI into the physical layer is a cornerstone of 6G networks. However, current data-driven approaches struggle to generalize across dynamic environments because they lack an intrinsic understanding of electromagnetic wave…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
We present sum-set inequalities specialized to the generalized degrees of freedom (GDoF) framework. These are information theoretic lower bounds on the entropy of bounded density linear combinations of discrete, power-limited dependent…
A Gabor system generated by a window function $g\in L^2(\mathbb{R}^d)$ and a separable set $\Lambda\times \Gamma \subset \mathbb{R}^{2d}$ is the collection of time-frequency shifts of $g$ given by $\mathcal G(g, \Lambda\times \Gamma) =…
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…
We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces H . More precisely, we determine whether a given frame…
We consider the problem of estimating local sensor parameters, where the local parameters and sensor observations are related through linear stochastic models. Sensors exchange messages and cooperate with each other to estimate their own…
In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet frames for the extended affine group. Firstly, we give necessary and sufficient conditions for the existence of nonstationary frames of translates. Using these…
In this note we study frame-related properties of a sequence of functions multiplied by another function. In particular we study frame and Riesz basis properties. We apply these results to sets of irregular translates of a bandlimited…
The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…
Wireless sensing is of great benefits to our daily lives. However, wireless signals are sensitive to the surroundings. Various factors, e.g. environments, locations, and individuals, may induce extra impact on wireless propagation. Such a…
Generative Artificial Intelligence (GenAI) has made significant advancements in fields such as computer vision (CV) and natural language processing (NLP), demonstrating its capability to synthesize high-fidelity data and improve…
Newer cellular communication generations are planned to allow asynchronous transmission of multiple numerologies (waveforms with different parameters) in adjacent bands, creating unavoidable adjacent channel interference. Most prior work on…
One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the…
We extend the concept of weaving Hilbert space frames to the Banach space setting. Similar to frames in a Hilbert space, we show that for any two approximate Schauder frames for a Banach space, every weaving is an approximate Schauder frame…
Configurations of subspaces like equichordal and equiisoclinic tight fusion frames, which are in some sense optimally spread apart and which also have reconstruction properties emulating those of orthonormal bases, are useful in various…
Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected…
We consider statistical graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. This general model encompasses various signals such as the traditional…