Related papers: Trigonometric splines in spectral problems
We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schr\"odinger equation with a spatially and temporally random potential. Green's functions for the…
The scattering of electromagnetic pulses is described using a non-singular boundary integral method to solve directly for the field components in the frequency domain, and Fourier transform is then used to obtain the complete space-time…
Singular Spectrum Analysis and many other subspace-based methods of signal processing are implicitly relying on the assumption of close proximity of unperturbed and perturbed signal subspaces extracted by the Singular Value Decomposition of…
The interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive…
Interdependencies between experimental spectra, representing line or plane projections of electronic densities, are derived from their consistency and symmetry conditions. Some additional relations for plane projections are obtained by…
In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven…
Terahertz time-domain spectroscopy (THz TDS) is a well-known tool for material analysis in the terahertz frequency band. One crucial system component in every time-domain spectrometer is the delay line which is necessary to accomplish the…
An ever-looming threat to astronomical applications of machine learning is the danger of over-fitting data, also known as the `curse of dimensionality.' This occurs when there are fewer samples than the number of independent variables. In…
X-ray speckles have been used for a wide variety of experiments, ranging from imaging (and tomography), wavefront sensing, spatial coherence measurements all the way to x-ray photon correlation spectroscopy (XPCS) and ptychography. In the…
The aim of this article is to present a time-frequency theory for orthogonal polynomials on the interval [-1,1] that runs parallel to the time-frequency analysis of bandlimited functions developed by Landau, Pollak and Slepian. For this…
The importance of ultrasound is well established in the imaging of human tissue. In order to enhance image quality by exploiting nonlinear effects, recently techniques such as harmonic imaging and nonlinearity parameter tomography have been…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
A novel approach towards the spectral analysis of stationary random bivariate signals is proposed. Using the Quaternion Fourier Transform, we introduce a quaternion-valued spectral representation of random bivariate signals seen as…
In this thesis, the numerical solution of three different classes of problems have been studied. Specifically, new techniques have been proposed and their theoretical analysis has been performed, accompanied by a wide set of numerical…
We study light curves and the spectral broadening of the radiation emitted during the finite interval of time by a surface of a collapsing object. We study a simplified model of monochromatic radiations from a spherical surface which is…
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…
We establish several fundamental properties of analysis-suitable T-splines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended…
We describe extensive computational experiments on spectral properties of random objects - random cubic graphs, random planar triangulations, and Voronoi and Delaunay diagrams of random (uniformly distributed) point sets on the sphere). We…
The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…
Two iterative techniques are described for decomposing a long-slit spectrum into the individual spectra of the point sources along the slit and the spectrum of the underlying background. One technique imposes the strong constraint that the…