Frequently it is desirable to know the statistical properties of the output of certain frequency sensitive devices when some type of random signal is impressed. Since most devices of this type are followed by low pass filters, this problem is one of determining the statistics of a filtered signal.The problem of finding the probability density of the difference of two dependent random variables has not been solved in any general way. Also, the problem of finding the statistical properties of the output of a linear filter upon which a non‐Gaussian random signal is impressed has been considered by only a very few writers.The first sections of this paper gives a solution of the case of a frequency discriminator with no low pass filter, excited by a narrow band spectrum, and is solved by expressing the output of the device as the difference of two independent random quantities, which allows the use of the characteristic function method.The later sections contain a solution of the problem when a low pass filter is present at the discriminator output. This is done by obtaining the predominant moments of the density from a series expansion which gives a good approximation to the nature of that density Also, in this regard, the approach of the density to a Gaussian one, as the output filter band is made very narrow, is clearly shown.