Related papers: Exponential Approximation of Bandlimited Random Pr…
Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…
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.…
We consider the reconstruction of a bandlimited function from its finite localized sample data. Truncating the classical Shannon sampling series results in an unsatisfactory convergence rate due to the slow decay of the sinc function. To…
We consider the problem of reconstructing a wide sense stationary band-limited process from its local averages taken either at the Nyquist rate or above. As a result, we obtain a sufficient condition under which average sampling expansions…
Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an…
We consider the reconstruction of a bandlimited function from its finite localized sample data. Truncating the classical Shannon sampling series results in an unsatisfactory convergence rate due to the slow decayness of the sinc function.…
In this paper, we discuss some numerical realizations of Shannon's sampling theorem. First we show the poor convergence of classical Shannon sampling sums by presenting sharp upper and lower bounds of the norm of the Shannon sampling…
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 fast reconstruction of a bandlimited function from its sample data is an essential problem in signal processing. In this paper, we consider the widely used Gaussian regularized Shannon sampling formula in comparison to regularized…
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…
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…
Due to excessive need for faster propagations of signals and necessity to reduce number of measurements and rapidly increase efficiency, new sensing theories have been proposed. Conventional sampling approaches that follow Shannon-Nyquist…
The classical sampling Nyquist-Shannon-Kotelnikov theorem states that a band-limited continuous time function can be uniquely recovered without error from a infinite two-sided sampling series taken with a sufficient frequency. This short…
Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker--Kotel'nikov--Shannon (WKS) sampling restoration sum for Bernstein function classes $B_{\pi,d}^q,\, q>1,\, d\in \mathbb N$, when…
The paper investigates possibility of recovery of sequences from their decimated subsequences. It is shown that this recoverability is associated with certain spectrum degeneracy of a new kind, and that a sequences of a general kind can be…
Shannon's sampling theorem is one of the cornerstone topics that is well understood and explored, both mathematically and algorithmically. That said, practical realization of this theorem still suffers from a severe bottleneck due to the…
Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields. In this survey we present several extensions of the Shannon…
The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates $L_p([0,T])$ and uniform approximations of…
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…
Shannon's sampling theorem provides a link between the continuous and the discrete realms stating that bandlimited signals are uniquely determined by its values on a discrete set. This theorem is realized in practice using so called…