DTIC ADA1010985: Statistics of Nonlinearly Transformed Coherence pdf

DTIC ADA1010985: Statistics of Nonlinearly Transformed Coherence

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Description of the Book:

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

• Creator/s: Defense Technical Information Center
• Date: 3/12/1981
• Year: 1981
• Book Topics/Themes: DTIC Archive, Nuttall, Albert H, NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT, *ASYMPTOTIC SERIES, *COHERENCE, *NONLINEAR SYSTEMS, *STATISTICAL ANALYSIS, *TRANSFORMATIONS(MATHEMATICS), ANALYSIS OF VARIANCE, APPROXIMATION(MATHEMATICS), BIAS, DATA REDUCTION, ERROR ANALYSIS, ESTIMATES, EXPONENTIAL FUNCTIONS, MEAN, PROBABILITY DENSITY FUNCTIONS

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