Notice that we have assumed that the modulating signal is sinusoidal
to make the analysis easy. In real life, m(t) is a non sinusoidal,
band-limited signal—its frequency spectrum is within the range between
0 and ωu = 2πfu (i.e., the signal has an upper frequency limit). Typically,
fu = 5 kHz for AM radio. If the frequency spectrum of the modulating
signal is as shown in Fig. 17.24(a), then the frequency spectrum of the
AM signal is shown in Fig. 17.24(b). Thus, to avoid any interference,
carriers for AM radio stations are spaced 10 kHz apart.