Figures 5.20 and 5.21 illustrate the changes in the modulated carrier spectrum as
the modulation index is increased for a Gaussian modulating signal. One can see that
for a high modulation index the frequency deviation is given by FM
√
PM and the
bandwidth is approximated by BW = 2FM
√
PM, in order to include most of the
modulated carrier power. As previously derived, the bandwidth for a narrowband FM
is BW = 2ωM. Interpolating between both values gives a formula that covers the whole
range of modulation indices β: