FigureP.7.I8 shows a carrier of frequency ωc being amplitude-modulated by a sine wave of f...

FigureP.7.I8 shows a carrier of frequency ωc being amplitude-modulated by a sine wave of frequency ωm, that is,

E = E0(l + a cos ωmt) cos ωct

Show that this is equivalent to the superposition of three waves of frequencies ωc, ωc+ ωm, and ωc-ωm. When a number of modulating frequencies are present, we write E as a Fourier series and sum over all values of ωm. The terms ωc+ ωm constitute what is called the upper sideband, and all the ωc- ωm terms form the lower sideband.

What bandwidth would you need in order to transmit the complete audible range?

Figure