Optimum sampling for estimation of Fourier coefficients in noise

The problem of optimum sampling strategies for spectral estimation of Fourier-type signals from a finite number of noisy discrete-time observations was investigated. It was shown that equally spaced sampling is among the optimum set of times for finding minimum variance unbiased estimates of the coefficients of a single sinusoid imbedded in additive zero-mean noise. It was also shown for the white noise case that samples taken at a nonuniform rate could be used to estimate the values of the signal at the uniform sample times reducing the variances of these estimates by the ratio of Nyquist rate to average sample rate.