Amplitude modulation, or AM, makes the amplitude of a carrier vary with a message signal.

A conventional AM waveform can be written

$$s(t)=A_c[1+\mu m_n(t)]\cos(2\pi f_ct),$$

where $m_n(t)$ is a normalized message and $\mu$ is the modulation index.

The carrier term produces a spectral component at $f_c$. Multiplication of the message by the carrier creates two translated copies of the message spectrum: the upper and lower sidebands.

If the message is band-limited to $B$ hertz, ordinary double-sideband AM occupies approximately

$$2B$$

hertz around the carrier.

For envelope detection to recover the message without envelope inversion, the modulation depth must stay within the range that keeps the carrier envelope from crossing through zero.

AM is therefore a way to place a baseband message into a passband by encoding it in the carrier amplitude and its sidebands.