Concept

Nyquist–Shannon sampling theorem

Related publications (268)

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Sampling signals with finite rate of innovation

Martin Vetterli, Pina Marziliano, Thierry Blu

Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform ...

Institute of Electrical and Electronics Engineers2002

Sampling of Periodic Signals: A Quantitative Error Analysis

Michaël Unser, Thierry Blu, Mathews Jacob

We present an exact expression for the

L _{ 2 }

error that occurs when one approximates a periodic signal in a basis of shifted and scaled versions of a generating function. This formulation is applicable to a wide variety of linear approximation schem ...

IEEE2002

Power spectra of random spike fields and related processes

Andrea Ridolfi, Pierre Bremaud

This paper presents general methods for obtaining power spectra of a large class of signals and random fields driven by an underlying point processes, in particular spatial shot noises with random impulse response and arbitrary basic stationary point proce ...

2002

A generalized Rate-Distortion limit for edge representation

Pierre Vandergheynst, Lorenzo Granai

This paper presents a rate-distortion analysis for a simple horizon edge image model. A quadtree with anisotropy and rotation is performed in this kind of image, giving a toy model for a non-linear adaptive coding technique, and its rate-distortion behavio ...

2002

A sampling theorem for periodic piecewise polynomial signals

Martin Vetterli, Pina Marziliano, Thierry Blu

We consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomials. We demonstrate that by using an adequate sampling kernel and a sampli ...

2001

On simple oversampled A/D conversion in L2(R)

Martin Vetterli

Accuracy of oversampled analog-to-digital (A/D) conversion, the dependence of accuracy on the sampling interval, t, and on the bit rate are characteristics fundamental to A/D conversion but not completely understood. These characteristics are studied in th ...

Institute of Electrical and Electronics Engineers2001

Method for sending information signals over a communication channel, and corresponding encoder

Bixio Rimoldi

Pulse amplitude modulation scheme with the same spectral efficiency as QAM, that is twice the spectral efficiency of conventional PAM schemes, comprising the steps of: (1) forming a train of pulses q(t -kT/2) = p(t - k T/2)cos2 pi fo(t- k T/2), wherein p(t ...

2001

Generalized Sampling: A Variational Approach

Michaël Unser, Thierry Blu

We consider the problem of reconstructing a multidimensional and multivariate function ƒ:

ℜ ^{ m }

\rightarrow

ℜ ^{ n }

from the discretely and irregularly sampled responses of q linear shift-invariant filters. Unlike traditional approaches which r ...

SampTA2001

Reconstruction of irregularly sampled discrete-time bandlimited signals with unknown sampling locations

Martin Vetterli, Pina Marziliano

The purpose of this paper is to develop methods that can reconstruct a bandlimited discrete-time signal from an irreg- ular set of samples at unknown locations. We define a solution to the problem using first a geometric and then an algebraic point of view ...

2000

Sampling—50 Years After Shannon

Michaël Unser

This paper presents an account of the current state of sampling, 50 years after Shannon's formulation of the sampling theorem. The emphasis is on regular sampling where the grid is uniform. This topic has benefited from a strong research revival during the ...

IEEE2000