Related papers: On Nyquist-Shannon Theorem with one-sided half of …
The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel's entanglement assisted classical capacity. In…
We present an elementary proof of the classical Beurling sampling theorem which gives a sufficient condition for sampling of multi-dimensional band-limited functions.
The Whittaker-Shannon-Kotel'nikov (WSK) sampling theorem provides a reconstruction formula for the bandlimited signals. In this paper, a novel kind of the WSK sampling theorem is established by using the theory of quaternion reproducing…
We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either…
We study the problem of sampling a random signal with sparse support in frequency domain. Shannon famously considered a scheme that instantaneously samples the signal at equispaced times. He proved that the signal can be reconstructed as…
The identification of sampling sets that enable unique signal recovery is fundamental to many applications in signal processing and remains a central problem in mathematical analysis. Recent studies in the mathematical literature,…
Signal sampling and reconstruction is a fundamental engineering task at the heart of signal processing. The celebrated Shannon-Nyquist theorem guarantees perfect signal reconstruction from uniform samples, obtained at a rate twice the…
We show that bandlimited signals can be uniquely recovered (up to a constant global phase factor) from Gabor transform magnitudes sampled at twice the Nyquist rate in two frequency bins.
Universal (pointwise uniform and time shifted) truncation error upper bounds are presented in Whittaker--Kotel'nikov--Shannon (WKS) sampling restoration sum for Bernstein function class $B_{\pi,d}^q\,,\ q \ge 1,$ $d\in \mathbb N\,,$ when…
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…
Sampling is classically performed by recording the amplitude of an input signal at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the…
Consider a source E of pure quantum states with von Neumann entropy S. By the quantum source coding theorem, arbitrarily long strings of signals may be encoded asymptotically into S qubits/signal (the Schumacher limit) in such a way that…
We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating…
This paper deals with the problem of reconstructing a band-limited signal when a finite subset of its samples and of its derivative are missing. The technique used, due to P.J.S.G. Ferreira, is based on the use of a particular frame for…
For a continuous-time additive white Gaussian noise (AWGN) channel with possible feedback, it has been shown that as sampling gets infinitesimally fine, the mutual information of the associative discrete-time channels converges to that of…
It has been observed by several authors that well-known periodization strategies like tent or Chebychev transforms lead to remarkable results for the recovery of multivariate functions from few samples. So far, theoretical guarantees are…
This paper introduces Manhattan sampling in two and higher dimensions, and proves sampling theorems. In two dimensions, Manhattan sampling, which takes samples densely along a Manhattan grid of lines, can be viewed as sampling on the union…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
The product of any number of Legendre functions, under a restricted domain, can be expanded by the corresponding Legendre polynomials, with the coefficient being the sinc function. While an analogous expansion can be made for any number of…
A finite sequence of equidistant samples (a sample train) of a periodic signal can be identified with a point in a multi-dimensional space. Such a point depends on the sampled signal, the sampling period, and the starting time of the…