Theoretical evaluation of the performance of a random power spectrum analyzer

This paper deduces the theoretical performance of a power spectrum analyzer based on the evaluation of the autocorrelation function of a periodic signal. This autocorrelation is estimated through a random sampling strategy previously introduced by the authors. The estimator uncertainty is deduced by evaluating the asymptotic statistical parameters of the output; it is shown that the asymptotic mean is unbiased and the expression of the asymptotic mean square error is deduced. From this last it is proved that the proposed sampling strategy doesn´t introduce any bandwidth limitation. The experimental results through the simulation of the instrument performance are in complete agreement with the theoretical findings