Editing Amplitude modulation (section)

==Spectrum==
[[File:AM spectrum.svg|thumb|400px|Figure 2: Double-sided spectra of baseband and AM signals.|alt=Diagrams of an AM signal, with formulas]]
A useful modulation signal ''m(t)'' is usually more complex than a single sine wave, as treated above. However, by the principle of [[Fourier decomposition]], ''m(t)'' can be expressed as the sum of a set of sine waves of various frequencies, amplitudes, and phases. Carrying out the multiplication of  ''1 + m(t)'' with ''c(t)'' as above, the result consists of a sum of sine waves. Again, the carrier ''c(t)'' is present unchanged, but each frequency component of ''m'' at ''f<sub>i</sub>'' has two sidebands at frequencies ''f<sub>c</sub> + f<sub>i</sub>'' and  ''f<sub>c</sub> – f<sub>i</sub>''. The collection of the former frequencies above the carrier frequency is known as the upper sideband, and those below constitute the lower sideband. The modulation ''m(t)'' may be considered to consist of an equal mix of positive and negative frequency components, as shown in the top of figure 2. One can view the sidebands as that modulation ''m(t)'' having simply been shifted in frequency by ''f<sub>c</sub>'' as depicted at the bottom right of figure 2.

[[File:AM signal.jpg|thumb|200px|right|Figure 3: The [[spectrogram]] of an AM voice broadcast shows the two sidebands (green) on either side of the carrier (red) with time proceeding in the vertical direction.|alt=Sonogram of an AM signal, showing the carrier and both sidebands vertically]]
The short-term spectrum of modulation, changing as it would for a human voice for instance, the frequency content (horizontal axis) may be plotted as a function of time (vertical axis), as in figure 3. It can again be seen that as the modulation frequency content varies, an upper sideband is generated according to those frequencies shifted ''above'' the carrier frequency, and the same content mirror-imaged in the lower sideband below the carrier frequency. At all times, the carrier itself remains constant, and of greater power than the total sideband power.