Theory of Low-Distortion Reproduction of FM Signals in Linear Systems

Certain fundamental aspects of linear-system response to variable-frequency excitations are discussed. A unified argument is presented to simplify the derivation and define the convergence properties of the Carson and Fry and van der Pol-Stumpers expansions. Upper bounds on errors incurred in restricting each expansion to a finite number of terms are derived. This analysis leads to a more complete, more general statement of the conditions for low-distortion transmission and FM-to-AM conversion of FM signals than has heretofore been published. This statement shows that the most significant property of a frequency modulation is its maximum slope, and that the sluggishness properties of a linear system are completely specified by its "sluggishness ratio,"
| Z"(j{\omega})/Z(j{\omega})|
, where
Z(j{\omega})
is the system function. Plots of this ratio for various important filters are presented. The newly derived condition for quasi-stationary response is proposed as a more complete criterion for specifying FM system bandwidths, and an analysis of the distortion in the quasi-stationary response is presented.