On the sampling rate issue in spectral analysis

The fundamental difficulty in the resolution of closely spaced modes using parametric spectral estimation techniques is shown to be a numerical one. Using the condition number of the sampled covariance matrix, an optimal sampling rate for the covariance function is derived. It is shown that by employing the optimal sampling rate, frequency resolution can be significantly improved. The optimization of the sampling rate is subsequently extended to rates smaller than the Nyquist rate. This yields a "zoom in" procedure which enables the resolution of very close modes in high noise.