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Power spectrum of a pulse train specified by its probability-generating function

Power spectrum of a pulse train specified by its probability-generating function

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A stationary stochastic train of nonoverlapping pulses is considered, and a link is established between the conditional probability density pk(τ) for the appearance of k successive count-to-count intervals during the time interval τ, assuming that the first count-to-count interval has begun (with the first pulse) at t = 0, and that the kth interval has ended (with the last pulse) at t = τ, and the probability Gj(τ) that j successive pulses of this train will appear during the same time interval τ (supposing that the initial time t = 0 has been selected at random). If the train considered consists of identical unit pulses, it is also possible to relate to Gj(τ) its autocorrelation function R(τ), as well as its power density P(ω).

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