If

and

are statistically independent stationary Gaussian random processes, each having correlation function

, mean squared value

, and spectral density

, then

is a stationary Gaussian random process with correlation function

and with spectral density

, symmetric about

for large

. From this representation of

it is shown that the variance of the number of zeros of

in the interval

is, for integral

,

. This result complements that of Steinberg, {em et al.}, giving var

for wide-band Gaussian noise. The limit of

as

is evaluated for several spectra, and expressions are found for the variance of the number of zeros of the sum of the foregoing narrowband noise plus a sinusoid of frequency

. From these results the low-frequency output spectral density of an FM receiver is obtained. Below the threshold the output signal-to-noise ratio is found to be

, where

is the input signal-to-noise ratio,

is the rms frequency deviation, assumed small enough not to affect the output noise, and

is the output bandwidth, assumed small compared to the input bandwidth. By the addition of the well known "triangular" noise, this expression is made valid through and above the threshold, thus unifying various results of Rice. The quieting of a wide-band FM receiver by a signal is also considered.