The Waterbed Effect in Spectral Estimation

In this lecture note, we present a textbook-like derivation of the waterbed effect result in Ninness (2003). Compared with Ninness, our analysis is much simpler and yet slightly more general in that it is not limited to rational spectral densities as in Ninness (it is noted, however, that Ninness has also derived a closed-form expression for the finite-m CRB on the relative variance of Φ(ω, θˆ), which we do not).