Approximate bounds on frequency estimates for short cisoids in colored noise

It is demonstrated that the Cramer-Rao lower bounds on frequency estimates for short data records containing cisoids in colored Gaussian noise are well approximated by simple formulas based on a white noise assumption, suitably modified to account for the local noise levels at the cisoidal frequencies. The approximations are accurate to within a few tens of percent, even for records with as few as ten data points, provided the noise spectra are reasonably smooth over frequency intervals corresponding to 2π times the reciprocal of the number of data points