Best linear unbiased estimation of the Fourier coefficients of periodic signals

Fourier coefficients of periodic signals are usually estimated by the discrete Fourier transform (DFT). Since DFT is equivalent to ordinary least squares, it might be expected to be best linear unbiased only if the errors in the observations are not covariant. Fortunately, for covariant errors, the DFT achieves this optimum property asymptotically