Statistics of Nonlinearly Transformed Coherence Estimates

Abstract

An asymptotic relation for the average value of any nonlinear transformation of a magnitude-squared-coherence estimate is derived. It is utilized to determine the bias, variance, and mean-square error of the transformed coherence estimate. It is found that the arc tanh (x(1/2)) transformation is the only one with variance independent of the true coherence value to O(N(-1)), and that the 1n(x) transformation is the only one with zero bias, to exponential order in N. Here, N is the number of data pieces employed in the estimation of the coherence. Extensions to terms of O(N(-2)) are made and presented for a v-th law device also.

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Document Details

Document Type
Technical Report
Publication Date
Mar 12, 1981
Accession Number
ADA101098

Entities

People

  • Albert H. Nuttall

Organizations

  • Naval Underwater Systems Center

Tags

Communities of Interest

  • C4I
  • Weapons Technologies

DTIC Thesaurus Topics

  • Asymptotic Series
  • Coefficients
  • Confidence Limits
  • Curve Fitting
  • Data Science
  • Equations
  • Hypergeometric Functions
  • Information Science
  • Integrals
  • Plastic Explosives
  • Power Series
  • Probability
  • Probability Density Functions
  • Random Variables
  • Signal Processing
  • Statistics
  • Universities

Fields of Study

  • Engineering
  • Mathematics

Readers

  • Statistical inference.