Any complex waveform can be broken into its component sine waves.The same is true for an amplitude modulated waveform such as that shown in Fig.15.This wave is for instance a 700KHz carrier modulated by,for instance,a 2KHz sine wave.A waveshape of this type is the one at the output of the diode modulator already studied in Worksheet No.1.
If we had a tunable band-pass filter or a spectrum analyzer we could search the spectrum and determine which frequencies are contained in the modulated signal.Doing this,we would find a signal at 698KHz and another at 702KHz,in addition to the carriersignal at 700KHz.These two signals are called side-bands,respectively Upper and Lower side-bands.
The side-bands can be extracted from a modulated waveform by using a sharply tuned filter.