The spectrum of frequency-modulated waves after reception in random noise-I
David Middleton · Quarterly of Applied Mathematics · 1949
Part I: Introduction and DiscussionThe reception of radio, radar, and television signals is always accomplished in the presence of noise, which exclusive of outside sources-either man-made or naturalarises because of the random motion of electrons in the various circuit elements of the receiver, principally in the stages preceding the detecting devices.The noise is accordingly assumed to be of the fluctuation type; impulse noise is not considered in this paper.Knowledge of the spectral distribution and the power output following demodulation of a frequency-modulated carrier in such noise is essential to any critical theory of receiver behavior.Accordingly, the principal purpose of the present work is to investigate the spectral aspects of the problem.One of the chief reasons for our interest in the spectrum lies in the fact that the signal-to-noise ratio at the output as a function of the ratio at the input depends markedly on the spectral distribution, in the so-called case of broad-band FM (where the maximum change in carrier frequency may be several times the highest modulating components).The dependence in the instance of narrowband FM (for which the maximum deviation in the carrier frequency is comparable with or less than the highest significant audio modulating frequency) is not nearly so critical.Previous investigations, of which the work of Carson and Fry,1 Crosby,2 Blachman,3 and Rice4 are particularly to be noted here,** have dealt chiefly with the strong-carrier case, in which the noise is largely suppressed and appears linearly with the signal in *