Spectral Characteristics of FDM-FM Signals

The power spectrum of a sinusoidal carrier which is frequency modulated by a normally distributed baseband signal may be expanded as a sum of weighted convolution terms. The significant parameter in the expansion, for an ideally bandlimited baseband spectrum, is
R_{x}(0) = R_{\dot{x}}(0)/f
min
f
max where
R_{\dot{x}}(0)
is the mean squared frequency deviation and
f
min and
f
max are the lower and upper frequency limits of the baseband spectrum. For small values of
R_{x}(0)
, the spectrum may be approximated using the baseband and the carrier. For large
R_{x}(0)
, the spectrum is asymptotically Gaussian. We have computed spectra on a digital computer for intermediate values of
R_{x}(0)
. In all computations, the spectra are approximated by ten convolution terms, defining the carrier component as the first term. Computations are for
R_{x}(0) = 1, 2, 3, 4, 5
for a rectangular baseband spectrum with no pre-emphasis and with CCIR pre-emphasis. The results are for typical multichannel FDMFM bands 12 to 36 kHz, 12 to 60 kHz, 12 to 156 kHz, and 12 to 252 kHz.