Related papers: Beyond Bandlimited Sampling: Nonlinearities, Smoot…
In this work, we draw connections between the classical Shannon interpolation of bandlimited deterministic signals and the literature on estimating continuous-time random processes from their samples (known in various communities under…
The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem with fast decreasing coefficient, as well as a new modification of the corresponding interpolation formula applicable for general type non-vanishing bounded…
While nonlinear optical spectroscopy is becoming more commonly used to study the excited states of nonlinear-optical systems, a general theory of inhomogeneous broadening is rarely applied in lieu of either a simple Lorentzian or Gaussian…
We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
In the field of signal processing, the sampling theorem plays a fundamental role for signal reconstruction as it bridges the gap between analog and digital signals. Following the celebrated Nyquist-Shannon sampling theorem, generalizing the…
The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…
Deep neural networks (DNN) are the state of the art on many engineering problems such as computer vision and audition. A key factor in the success of the DNN is scalability - bigger networks work better. However, the reason for this…
We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features.…
Theory of nonlinear resonance, including stochastic one, is developed on the basis of the statistical field theory and using variables action-angle. Explicit expressions of action, proper frequency and nonlinearity parameter as functions of…
A theorem on subwavelength imaging with arrays of discrete sources is formulated. This theorem is analogous to the Kotelnikov (also named Nyquist-Shannon) sampling theorem as it represents the field at an arbitrary point of space in terms…
Resampling is an operation costly in calculation time and accuracy. It regularizes irregular sampling, replacing N data by N periodic estimations. This stage can be suppressed, using formulas built with incoming data and completed by…
Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or…
Both sampling a time-varying signal, and its spectral analysis are activities subjected to theoretically compelling, such as Shannon's theorem and the objectively limiting of the frequency's resolution. Usually, the signals' spectra are…
As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces…
The aim of this paper is to extend two results from the Paley--Wiener setting to more generalmodel spaces. The first one is an analogue of the oversampling Shannon sampling formula. The second one is a version of the Donoho--Logan Large…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
Reconstructing a band-limited function from its finite sample data is a fundamental task in signal analysis. A Gaussian regularized Shannon sampling series has been proved to be able to achieve exponential convergence for uniform sampling.…
This paper provides an extension of compressed sensing which bridges a substantial gap between existing theory and its current use in real-world applications. It introduces a mathematical framework that generalizes the three standard…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…