Average spectrum of a periodic series of identical pulses randomly displaced and distorted

It is shown that the resulting spectrum may be analysed into two parts. The first is the discrete spectrum corresponding to the basic pulse repetition frequency but with a modified amplitude function. These modifications depend in a rather intricate manner on the nature of the disturbances, with a substantial simplification when the shape and timing disturbances are independent. The second is a continuous spectrum which again is a function of both shift and distortion. It is suggested that the ratio of the energy in the two spectra has the same meaning as s./n. ratio.