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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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The normal, a continuous distribution, is the most important of all the distributions. Its graph is a bell-shaped symmetrical curve, which is observed in almost all disciplines. Some of these include psychology, business, economics, the sciences, nursing, and, of course, mathematics. Some instructors may use the normal distribution to help determine students’ grades. Most IQ scores are normally distributed. Often real-estate prices fit a normal distribution. The normal distribution is...
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Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes.

Jesús Gutiérrez-Gutiérrez1, Marta Zárraga-Rodríguez1, Pedro M Crespo1

  • 1Tecnun, University of Navarra, Paseo de Manuel Lardizábal 13, 20018 San Sebastián, Spain.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This paper introduces an integral formula for the rate distortion function (RDF) of Gaussian asymptotically wide sense stationary (AWSS) vector processes. The formula is then applied to derive specific RDF formulas for Gaussian moving average (MA) and autoregressive moving average (ARMA) processes.

Keywords:
ARMA vector processesAWSS vector processesGaussian vector processesMA vector processesrate distortion function

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Area of Science:

  • Information Theory
  • Signal Processing
  • Stochastic Processes

Background:

  • The rate distortion function (RDF) quantifies the fundamental limit of data compression for a given fidelity.
  • Calculating the RDF for complex stochastic processes, particularly vector processes, remains a significant challenge in information theory.

Purpose of the Study:

  • To derive a general integral formula for the RDF of Gaussian asymptotically wide sense stationary (AWSS) vector processes.
  • To extend this formula for specific classes of Gaussian vector processes, namely moving average (MA) and autoregressive moving average (ARMA) processes.

Main Methods:

  • Derivation of an integral formula for the RDF of Gaussian AWSS vector processes.
  • Application of the general formula to obtain specific integral formulas for Gaussian MA and ARMA vector processes.

Main Results:

  • An integral formula for the RDF of any Gaussian AWSS vector process has been obtained.
  • Integral formulas for the RDF of Gaussian MA and ARMA AWSS vector processes are derived as specific cases.

Conclusions:

  • The study provides a unified approach to calculating the RDF for a broad class of Gaussian vector processes.
  • The derived formulas offer valuable tools for analyzing and optimizing data compression schemes for these processes.