MODULATION

Over short distances, an information (baseband) signal carries enough energy on its own to be sent directly with no special processing -- a person's voice reaches a nearby listener without any electronics at all. Long-distance transmission is different: audio-frequency information (roughly 20 Hz to 20,000 Hz) cannot be radiated efficiently or reliably across the country or around the world in its raw form, so it must first be combined with a separate, very high-frequency radio signal called the carrier signal, through a process called modulation. The low-frequency baseband (input) signal is superimposed onto the high-frequency carrier, and because the carrier's frequency is so high, the combined signal can travel long distances with much lower attenuation, and is far more compatible with the transmission medium (free space) than the raw baseband signal would be on its own -- a carrier signal, on its own, carries no information at all; only once it is modulated by the baseband signal does it carry the message. A general sinusoidal carrier wave is written $e_c=E_c\sin(2\pi\nu_c t+\phi)$, where $E_c$ is its amplitude, $\nu_c$ its frequency, and $\phi$ its initial phase at time $t$. Exactly three characteristics of this carrier can be varied by the baseband signal during modulation -- its amp …