Related papers: Discrete Vector-Valued Nonuniform Gabor Frames
The transport of traffic flow can be modeled by the advection equation. Finite difference and finite volumes methods have been used to numerically solve this hyperbolic equation on a mesh. Advection has also been modeled discretely on…
Several applications of Internet of Things (IoT) technology involve capturing data from multiple sensors resulting in multi-sensor time series. Existing neural networks based approaches for such multi-sensor or multivariate time series…
This paper investigates first-order variable metric backward forward dynamical systems associated with monotone inclusion and convex minimization problems in real Hilbert space. The operators are chosen so that the backward-forward…
Irregularly sampling a spatially stationary random field does not yield a graph stationary signal in general. Based on this observation, we build a definition of graph stationarity based on intrinsic stationarity, a less restrictive…
Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not…
Modeling normal behavior in dynamic, nonlinear time series data is challenging for effective anomaly detection. Traditional methods, such as nearest neighbor and clustering approaches, often depend on rigid assumptions, such as a predefined…
2-D complex Gabor filtering has found numerous applications in the fields of computer vision and image processing. Especially, in some applications, it is often needed to compute 2-D complex Gabor filter bank consisting of the 2-D complex…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
We introduce a new class of frames with strong symmetry properties called geometrically uniform frames (GU), that are defined over an abelian group of unitary matrices and are generated by a single generating vector. The notion of GU frames…
The joint statistics of partial sums of ordered random variables (RVs) are often needed for the accurate performance characterization of a wide variety of wireless communication systems. A unified analytical framework to determine the joint…
The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights.…
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) =…
In this paper, $\mathcal{G}(g,L,M,N)$ denotes a $L-$window Gabor system on a periodic set $\mathbb{S}$, where $L,M,M\in \mathbb{N}$ and $g=\{g_l\}_{l\in \mathbb{N}_L}\subset \ell^2(\mathbb{S})$. We characterize which $g$ generates a…
Phasor measurement units (PMUs) are widely used for sub-synchronous oscillation monitoring, yet the effect of windowed discrete Fourier transform (DFT)-based phasor estimation on oscillation observability is not fully characterized. This…
The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that were considered unapproachable just a few years ago. However, in critical applications such…
The quantum Fourier transform for discrete variable (dvQFT) is an efficient algorithm for several applications. It is usually considered for the processing of quantum bits (qubits) and its efficient implementation is obtained with two…
Partition of unities appear in many places in analysis. Typically they are generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
We consider three problems for Gabor frames that have recently received much attention. The first problem concerns the approximation of dual Gabor frames in $L_2(R)$ by finite-dimensional methods. Utilizing Wexler-Raz type duality relations…
Graph signal processing has become an essential tool for analyzing data structured on irregular domains. While conventional graph shift operators (GSOs) are effective for certain tasks, they inherently lack flexibility in modeling…