Statistics of Nonlinearly Transformed Coherence Estimates
NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT
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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 x12 transformation is the only one with variance independent of the true coherence value to ON-1, and that the 1nx 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 ON-2 are made and presented for a v-th law device also.
- Statistics and Probability