Related papers: A guide on spectral methods applied to discrete da…
Classification is valuable and necessary in spectral analysis, especially for data-driven mining. Along with the rapid development of spectral surveys, a variety of classification techniques have been successfully applied to astronomical…
The unfolding of a gamma ray spectrum experience many difficulties due to noise in the recorded data, that is based mainly on the change of photon energy due to scattering mechanisms (either in the detector or the medium), the accumulation…
We investigate the potential of photonic lantern (PL) fiber fed spectrometers for two-dimensional spectroastrometry. Spectroastrometry, a technique for studying small angular scales by measuring centroid shifts as a function of wavelength,…
We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming…
Any frequency selective device with an ongoing drift will cause observed spectra to be variously and simultaneously scaled in proportion to their source distances. The reason is that detectors after the drifting selection will integrate…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free…
Sonography techniques use multiple transducer elements for tissue visualization. Signals detected at each element are sampled prior to digital beamforming. The required sampling rates are up to 4 times the Nyquist rate of the signal and…
This is the first article in a series of three dealing with the exploitation of speckle for imaging purposes. Speckle is the complex interference wave-field produced by a random distribution of un-resolved scatterers. In this paper, we show…
The asymptotic behavior of a one-dimensional spectral problem with periodic coefficient is addressed for high frequency modes by a method of Bloch wave homogenization. The analysis leads to a spectral problem including both microscopic and…
Multiple-frequency periodograms -- based on time series models consisting of two or more independent sinusoids -- have long been discussed. What is new here is the presentation of a practical, simple-to-use computational framework…
Spectral measurements in the infrared (IR) optical range provide unique fingerprints of materials which are useful for material analysis, environmental sensing, and health diagnostics. Current IR spectroscopy techniques require the use of…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation,…
Spectra derived from fast Fourier transform (FFT) analysis of time-domain data intrinsically contain statistical fluctuations whose distribution depends on the number of accumulated spectra contributing to a measurement. The tail of this…
Leveraging the intrinsic symmetries in data for clear and efficient analysis is an important theme in signal processing and other data-driven sciences. A basic example of this is the ubiquity of the discrete Fourier transform which arises…
In this paper, we propose a spectral method for deriving functions that are jointly smooth on multiple observed manifolds. This allows us to register measurements of the same phenomenon by heterogeneous sensors, and to reject…
The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…
Understanding the temporal characteristics of data from low frequency radio telescopes is of importance in devising suitable calibration strategies. Application of time series analysis techniques to data from radio telescopes can reveal a…