With the aid of an idealized representation of the discriminator, Middleton has shown that a frequency-modulated carrier remains intelligible for smaller carrier strengths when narrow-band f-m is used and the limiter is omitted than with a limiter and/or wideband f-m. It is, therefore, of some interest to treat the demodulation process as it actually occurs, in the absence of a limiter. Thus, the discriminator has been taken to consist of two selective circuits, both fed by the output of the intermediate-frequency amplifier, but peaked at different frequencies, feeding rectifiers whose outputs are subtracted. Each half of the device is treated in the manner used by Rice to determine the result of passing random noise and a sine wave through a rectifier; however, there is a correlation between the noise voltages fed to the two rectifiers.