Concept

Sinc function

Related publications (46)

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Isotropic Polyharmonic B-Splines: Scaling Functions and Wavelets

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

In this paper, we use polyharmonic B-splines to build multidimensional wavelet bases. These functions are nonseparable, multidimensional basis functions that are localized versions of radial basis functions. We show that Rabut's elementary polyharmonic B-s ...

IEEE2005

Error-Rate Dependence of Non-Bandlimited Signals with Finite Rate of Innovation

Ivana Jovanovic

We consider the rate-distortion problem for non-bandlimited signals that have a finite rate of innovation, in particular, the class of continuous periodic stream of Diracs, characterized by a set of time positions and weights. Previous research has only co ...

2004

Oversampled A/D Conversion of Non-Bandlimited Signals with Finite Rate of Innovation

Ivana Jovanovic

We consider the problem of A/D conversion for non-bandlimitedsignals that have a finite rate of innovation, in particular, theclass of continuous periodic stream of Diracs, characterized by aset of time positions and weights. Previous research has onlycons ...

2004

Wavelet Theory Demystified

Michaël Unser, Thierry Blu

In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wa ...

IEEE2003

High-Resolution Acquisition Methods for Wideband Communication Systems

Martin Vetterli, Irena Maravic

We consider the problem of low-complexity timing synchronization in digital receivers for DS-CDMA and UWB systems operating over channels with single or multiple propagation paths. We extend some of our recent sampling results for certain classes of non-ba ...

2003

Interpolation of Signals by Generalized Piecewise-Linear Multiple Generators

Michaël Unser, Thierry Blu

This paper presents an interpolation method based on shifted versions of two piecewise linear generators, which provides approximation order 2 like usual piecewise-linear interpolation; i.e., this method is able to represent the constant and the ramp exact ...

IEEE2003

Sampling innovations

Pina Marziliano

Sampling theory has prospered extensively in the last century. The elegant mathematics and the vast number of applications are the reasons for its popularity. The applications involved in this thesis are in signal processing and communications and call out ...

EPFL2002

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

Sampling of communications systems with bandwidth expansion

Martin Vetterli, Andrea Ridolfi

Many communication systems are {\em bandwidth-expanding}: the transmitted signal occupies a bandwidth larger than the {\em symbol rate}. The sampling theorems of Kotelnikov, Shannon, Nyquist et al. shows that in order to represent a bandlimited signal, it ...

2002

Sampling of Periodic Signals: A Quantitative Error Analysis

Michaël Unser, Thierry Blu, Mathews Jacob

We present an exact expression for the

L _{ 2 }

IEEE2002