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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 12, 1981
- Accession Number
- ADA101098
Entities
People
- Albert H. Nuttall
Organizations
- Naval Underwater Systems Center