#### Example AM Spectra

Equation (4.4) can be used to write down the spectral representation of
by inspection, as shown in Fig.4.12. In the example
of Fig.4.12, we have Hz and Hz,
where, as always,
. For comparison, the spectral
magnitude of an *unmodulated* Hz sinusoid is shown in
Fig.4.6. Note in Fig.4.12 how each of the two
sinusoidal components at Hz have been ``split'' into two
``side bands'', one Hz higher and the other Hz lower, that
is,
. Note also how the
*amplitude* of the split component is divided equally among its
two side bands.

Recall that was defined as the *second term* of
Eq.(4.1). The first term is simply the original unmodulated
signal. Therefore, we have effectively been considering AM with a
``very large'' modulation index. In the more general case of
Eq.(4.1) with given by Eq.(4.2), the magnitude of
the spectral representation appears as shown in Fig.4.13.

**Next Section:**

Bessel Functions