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Rice  has shown that the noise output of an FM discriminator may be assumed to be the sum of two uncorrelated components, a Gaussian term and a click term (Poisson shot noise of impulses) for large carrier-to-noise ratios (CNR). In this paper the click process is introduced and the output noise is modeled again as the sum of a Gaussian term and shot-noise term that are in general correlated. The autocorrelation of the click process is derived and is shown to reduce to that of a Poisson process for large CNR. The cross correlation between the two components is derived, and the assumption that the two components become uncorrelated for large CNR is verified. The power spectrum of the Gaussian plus correlated click noise is compared to the exact power spectrum of the total output noise of an FM discriminator. Only the case with no modulation is analyzed.