The problem of finding the power spectrum of a physical process consisting of linear superimposed random events is solved under the general condition of events correlated in a Markov chain. The statistical properties of the system are described in terms of a generalized Markov matrix which contains all the information about the correlations existing between elementary events. The conditions for the existence of a line spectrum component are discussed and the line intensity calculated. In paper II, typical examples of application to practical problems are also given.