Publication

On the necessary density for spectrum-blind nonuniform sampling subject to quantization

Michael Christoph Gastpar
2000
Conference Papers

Abstract

It is known that in the absence of distortion, the necessary sampling density for a multiband signal is given by its spectral occupancy. However, in general, the samples have to he acquired nonuniformly. There exist sampling patterns such that reconstruction is feasible even if the actual spectral support of the multiband signal is not known. If the samples are distorted, an increased sampling density may lead to a superior performance. In this paper, we consider the case of small distortion due to fine quantization of the samples, and we derive a necessary condition on the optimal sampling density.

Official source

https://infoscience.epfl.ch/entities/publication/2705f21a-c4e1-499e-87a2-396a1ec4ea6f

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Michael Christoph Gastpar
2000
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/2705f21a-c4e1-499e-87a2-396a1ec4ea6f

About this result

Related concepts (15)

Density estimation

In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population. A variety of approaches to density estimation are used, including Parzen windows and a range of data clustering techniques, including vector quantization.

Distortion

In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal representing sound or a video signal representing images, in an electronic device or communication channel. Distortion is usually unwanted, and so engineers strive to eliminate or minimize it. In some situations, however, distortion may be desirable.

Density

Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume: where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight.

Related publications (2)

On the necessary density for spectrum-blind nonuniform sampling subject to quantization

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