  Nonlinear evolution causes the galaxy power spectrum to become broadly
correlated over different wavenumbers. It is shown that prewhitening the power
spectrum - transforming the power spectrum in such a way that the noise
covariance becomes proportional to the unit matrix - greatly narrows the
covariance of power. The eigenfunctions of the covariance of the prewhitened
nonlinear power spectrum provide a set of almost uncorrelated nonlinear modes
somewhat analogous to the Fourier modes of the power spectrum itself in the
linear, Gaussian regime. These almost uncorrelated modes make it possible to
construct a near minimum variance estimator and Fisher matrix of the
prewhitened nonlinear power spectrum analogous to the Feldman-Kaiser-Peacock
estimator of the linear power spectrum. The paper concludes with summary
recipes, in gourmet, fine, and fastfood versions, of how to measure the
prewhitened nonlinear power spectrum from a galaxy survey in the FKP
approximation. An Appendix presents FFTLog, a code for taking the fast Fourier
or Hankel transform of a periodic sequence of logarithmically spaced points,
which proves useful in some of the manipulations.
