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 2/spl pi/ times the reciprocal of the number of data points.