Spectral estimation of a Gaussian signal sampled with jitter

This article tackles the problem of a Gaussian band-limited continuous signal with unknown characteristics sampled with jitter. Under this weak assumption, we demonstrate a relation linking the power spectral density of the continuous signal to the second and fourth order statistics of the measured samples. A fundamental point is that this relation does not require a knowledge of the jitter characteristics. This result can be exploited for the derivation of spectral estimation algorithms when the jitter is unknown or jitter detection tests when the sampled signal is unknown. A simulation of spectral estimation confirms the validity of the result.