Complex Exponential Modulation
Many communication systems rely on the concept of sinusoidal amplitude modulation, in which a complex exponential or a sinusoidal signal, $ c(t)\! $, has its amplitude modulated by the information-bearing signal, $ x(t)\! $. $ x(t)\! $ is the modulating signal, and $ c(t)\! $ is the carrier signal. The modulated signal, $ y(t)\! $, is the product of these two signals:
An important objective of amplitude modulation is to produce a signal whose frequency range is suitable for transmission over the communication channel that is to be used.
One important for of modulation is when a complex exponential is used as the carrier.
