  We study the physical limitations placed on CMB temperature and polarization
measurements of the initial power spectrum by geometric projection, acoustic
physics, gravitational lensing and the joint fitting of cosmological
parameters. Detailed information on the spectrum is greatly assisted by
polarization information and localized to the acoustic regime k = 0.02-0.2
Mpc^{-1} with a fundamental resolution of Delta k/k>0.05. From this study we
construct principal component based statistics, which are orthogonal to
cosmological parameters including the initial amplitude and tilt of the
spectrum, that best probe deviations from scale-free initial conditions. These
statistics resemble Fourier modes confined to the acoustic regime and
ultimately can yield ~50 independent measurements of the power spectrum
features to percent level precision. They are straightforwardly related to more
traditional parameterizations such as the the running of the tilt and in the
future can provide many statistically independent measurements of it for
consistency checks. Though we mainly consider physical limitations on the
measurements, these techniques can be readily adapted to include instrumental
limitations or other sources of power spectrum information.
