Shape and duration of clicks in modulated FM transmission

Slepian model is derived for the shape of dicks in modulated FM transmission. The modulated signal may be a deterministic periodic function or a stationary stochastic process, not necessarily Gaussian. To describe the clicks one first derives the stochastic properties of noise and signal at the clicks. (For a periodic signal this amounts to giving the relative number of clicks in any given part of the period.) Then the conditional distributions of noise and signal near clicks are derived in explicit form, using the noise and signal values at the click as (random) parameters, and finally these conditional distributions are mixed into a total model for the click shapes. For increasing carrier-to-noise power ratioA^{2}/2, the Slepian model converges after normalization to a rational function with random coefficients. The amplitude of a click is shown to be of the orderA^{2}, in contrast to the unmodulated ease, where click amplitudes are of the orderA.