Distortion of FM Signals Caused by Channel Phase Nonlinearity and Amplitude Fluctuation

The distortion of FM (frequency-modulated) signals after being processed through time-invariant channels with nonlinear phase characteristic and/or fluctuating amplitude function is considered, starting from a Fourier spectral analysis of the signal. Expressions for calculating the distortion power or harmonic amplitudes, applicable to both single-tone and multitone message signals, are derived in terms of coefficients in the power series representation of channel phase characteristics. The quasi-stationary method is shown to be correct only in the leading term in each order of the distortion voltage. The missing terms can cause substantial errors in certain instances. Fluctuation in the channel amplitude function vs. frequency also causes change in the phase of the signal; the distortion generated is, however, one order of magnitude lower. Using a Butterworth-type bandpass filter as a particular example, the third and fifth harmonic amplitudes in the discriminator output are hand-calculated and plotted as a function of the modulation index. Results agree quite well with recent data from digital machine computations by Schenck and Kennedy. The spectral technique is also used to compute the channel bandwidth requirement, based on distortion considerations, and a family of curves is plotted from results of numerical computations on a digital computer.