"On random phase" [comments on A. Papoulis]
R. Esposito · Proceedings of the IEEE · 1965
With reference to the above-named correspondence by A. Papoulis [ibid., vol. 53, p. 526, May 1965] the commentor points out that in order to determine the density of the process z(t) = a sin (ωt + ϕ) it is not necessary to make the assumption that ϕ is independent of a. The necessary assumption (a much weaker one) is rather the stationarity of the conditional distribution ω(ϕ|a); it then follows that ϕ is independent of a and that the distribution of ϕ is uniform. This result was proved in 1958 by Bunkin and Gudzenko, as previously referred to by the commentor in the IRE PROCEEDIXGS [ibid., vol. 50, p. 1997, September 1962].