Related papers: Sampling Theorem and explicit interpolation formul…
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…
In this paper, we consider signal interpolation of discrete-time signals which are decimated nonuniformly. A conventional interpolation method is based on the sampling theorem, and the resulting system consists of an ideal filter with…
We study some problems related to the effect of bounded, additive sample noise in the bandlimited interpolation given by the Whittaker-Shannon-Kotelnikov (WSK) sampling formula. We establish a generalized form of the WSK series that allows…
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…
The paper studies spectral representation and its applications for non-decaying continuous time signals that are not necessarily bounded at $\pm\infty$. The paper introduces notions of transfer functions, spectrum degeneracy, spectrum gaps,…
Conventional sampling and interpolation commonly rely on discrete measurements. In this paper, we develop a theoretical framework for extrapolation of signals in higher dimensions from knowledge of the continuous waveform on bounded…
Sampling and reconstruction of functions is a central tool in science. A key result is given by the sampling theorem for bandlimited functions attributed to Whittaker, Shannon, Nyquist, and Kotelnikov. We develop an analogous sampling…
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…
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…
We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…
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 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…
In this paper, we study the problem of transient signal analysis. A signal-dependent algorithm is proposed which sequentially identifies the countable sets of decay rates and expansion coefficients present in a given signal. We…
We give a refined description of the dominant spectrum of a non-local operator that models growth and equal mitosis of cells. More precisely we look at the spectrum in half planes at the right hand side of the first accumulation point of…
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…
In our recent work, the sampling and reconstruction of non-decaying signals, modeled as members of weighted-$L_p$ spaces, were shown to be stable with an appropriate choice of the generating kernel for the shift-invariant reconstruction…
In this paper, we study the inverse scattering problem for a class of signals that have a compactly supported reflection coefficient. The problem boils down to the solution of the Gelfand-Levitan-Marchenko (GLM) integral equations with a…
We develop a formalism to describe squeezed light with large spectral-temporal correlations. This description is valid in all regimes, but is especially applicable in the long pulse to continuous-wave limit where the photon density at any…
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…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…