Expansions of Cumulative Distribution Functions Directly from Characteristic Functions

Abstract

Expansions of probability density functions and their corresponding cumulative distribution functions, directly from given characteristic functions, have been achieved in a series form, with four parameters which are under the control of the user, thereby enabling realization of more rapidly convergent terms. Typical examples of characteristic functions encountered in detection of multiple matched filter outputs are presented, along with an application to a noisy channel with partially correlated fading. The series presented here enable immediate evaluation of performance of a related normalizer once the expansion coefficients have been determined. An extension to allow for additive Gaussian noise is realized through a set of simple but efficient recursions.... Series expansions, Cumulative distributions, Characteristic functions, Rapid convergence, Fading application, Normalization

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Document Details

Document Type
Technical Report
Publication Date
Jun 08, 1993
Accession Number
ADA267727

Entities

People

  • Albert H. Nuttall

Organizations

  • Naval Undersea Warfare Center

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Coefficients
  • Detection
  • Distribution Functions
  • Gaussian Noise
  • Military Research
  • Noise
  • Observatories
  • Plastic Explosives
  • Power Series
  • Probability
  • Probability Density Functions
  • Random Variables
  • Research Facilities
  • Signal Processing
  • Surface Warfare
  • Warfare

Readers

  • Approximation Theory.
  • Radar Systems Engineering.