The power spectral density of the intensity of jittery trains after an integer temporal Talbot dispersive line is computed in the small-signal approximation. The influence in the spectrum of the optical linewidth and chirp of the Gaussian pulses of the train and also of different pulse-to-pulse timing jitter correlations is addressed. Before entering the Talbot dispersive line, timing jitter produces noise sidebands around the harmonics of the train. The temporal Talbot effect adds a multiplicative factor to the noise spectral density that depends on the characteristics of both the pulses and the dispersive line but not on the pulse-to-pulse correlation or the value of the timing jitter's standard deviation. The structure of this multiplicative term is peaked, resulting in narrowband noise patterns in specific locations of the spectrum and, in particular, around the harmonics of the train. Thus the temporal Talbot effect provides a dispersive mechanism for noise filtering. The bandwidth of the dispersion-induced noise peaks is ~1 order of magnitude below the repetition-rate frequency.