Evaluation of the Generalized QM Function for Complex Arguments

Abstract

Several possibilities for computing the generalized Q(sub M) (a, b) function for complex arguments a, b are presented and evaluated. Each approach has some limitations, such as loss of significance or complicated steepest paths of descent in an integral evaluation. However, a procedure is derived that will retain significance for all values of the parameters a, b, while avoiding underflow or overflow, and the procedures has been automated. The need for this function arises when the joint probability density function of the M- 1 largest squared envelopes of a matched filter output, plus the sum of the remainder, is considered. In particular, a Bromwich contour integral repeatedly utilizes this function in its evaluation.

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Document Details

Document Type
Technical Report
Publication Date
Aug 31, 2005
Accession Number
ADA439704

Entities

People

  • Albert H. Nuttall

Organizations

  • Naval Undersea Warfare Center

Tags

Communities of Interest

  • Air Platforms
  • Sensors

DTIC Thesaurus Topics

  • Bessel Functions
  • Complex Variables
  • Contour Integrals
  • Data Science
  • Distribution Functions
  • Equations
  • Information Science
  • Integrals
  • Matched Filters
  • Military Research
  • Numerical Integration
  • Power Series
  • Probability
  • Probability Density Functions
  • Random Variables
  • Statistics
  • Test And Evaluation

Readers

  • Approximation Theory.
  • Coastal and Marine Engineering/Sediment Transport/Hydraulic Engineering
  • Microwave Engineering.