Related papers: Finite equal norm Parseval Wavelet Frames over Pri…
Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…
This paper describes the limiting behavior of linear and decision feedback equalizers (DFEs) in single/multiple antenna systems employing real/complex-valued modulation alphabets. The wideband frequency selective channel is modeled using a…
We give a characterization of all Parseval wavelet frames arising from a given frame multiresolution analysis. As a consequence, we obtain a description of all Parseval wavelet frames associated with a frame multiresolution analysis. These…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…
We present a Parseval tight wavelet frame for the representation and analysis of velocity vector fields of incompressible fluids. Our wavelets have closed form expressions in the frequency and spatial domains, are divergence free in the…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…
We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal…
Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions,…
Factorization of matrices of Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction and filter bank design. Wavelet frames (a.k.a. framelets) are useful in applications such as signal…
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…
Interpolatory filters are of great interest in subdivision schemes and wavelet analysis. Due to the high-order linear-phase moment property, interpolatory refinement filters are often used to construct wavelets and framelets with high-order…
A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function.…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
One of the key challenges in the area of signal processing on graphs is to design transforms and dictionaries methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier…
We give a fairly comprehensive review of wavelets and of their application to density-functional theory (DFT) and to our recent application of a wavelet-based version of linear-response time-dependent DFT (LR-TD-DFT). Our intended audience…
This paper concerns the geometric structure of optimizers for frame potentials. We consider finite, real or complex frames and rotation or unitarily invariant potentials, and mostly specialize to Parseval frames, meaning the frame potential…
The emergence of alternative multiplexing domains to the time-frequency domains, e.g., the delay-Doppler and chirp domains, offers a promising approach for addressing the challenges posed by complex propagation environments and…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
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…