Certain mathematical representations of a limiter and discriminator are postulated. On this basis, and on the basis of the statistics of narrow‐band random noise, the output signal voltage and r.m.s. noise output voltage are calculated for a limiter and discriminator fed by an f‐m carrier and narrow‐band random noise. The output signal‐to‐noise ratio can thus be expressed as a function of the input signal‐to‐noise ratio. The former is plottedversusthe latter in Fig. 5, for several different degrees of limiting. A sharp increase in the output signal‐to‐noise ratio from far below the input signal‐to‐noise ratio to only 0.9 db below it is found to occur as the latter increases through the range 0 db to 6 db. For the sake of comparison, Fig. 5 also shows the corresponding curve for square law detection of an a‐m carrier, as well as that for f‐m without a limiter. It is to be emphasized that these results pertain to the unfiltered discriminator output; consideration of filtering, which is generally present in a receiver to a considerable extent, requires a determination of the spectral distribution of the discriminator output noise.