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.