My question came up while I was reading the book chapter "Multitaper Analysis of Nonstationary and Nonlinear Time Series Data" by David Thomson from the book Nonlinear and Nonstationary Signal Processing, copyright Cambridge University Press, 2000.
In the chapter Thomson describes a weighting function over a frequency interval of width $2W$ given by the current estimate of Fisher information of the spectrum estimator. If your current estimate of the spectrum is $\hat{S}$, then the estimate of Fisher information is given by:
$$\frac{Q_0(f')}{\hat{S}(f-f')}$$
$f'$ is a dummy variable for a convolution and $Q_0(f')$ is often given by $1 - (f'/W)^2$ , but not necessarily. I was wondering if anyone could help me with a derivation, because Thomson leaves it out completely.
The weighting function arises in the context of coherent side lobe subtraction.
