Sound is a relatively low-frequency signal that doesn’t travel far in air. So how does a radio transmit sound over longer distances? They shift the sound signals to a higher frequency band, with each radio station “mixing” the sound signal with a much higher frequency. Each station is assigned a specific frequency band, over which they send a high-frequency “carrier” containing information. When you tune into FM 100.3, you are listening to the frequency band centered around 100.3 MHz, the carrier frequency. The carrier frequency is chosen to be above the Nyquist frequency of 2 * {highest frequency that appears in the desired signal}, e.g. 44.1kHz for sound. This carrier wave is multiplied/added with the sound signal, or modified some other way, before being sent over the air. This modifying/mixing of the original signal is called modulation.
Because of trig product-to-sum identities, this doubles the bandwidth, with an upper and lower sideband that are each at half power.
$\cos(\omega)\cos(x) = \frac{1}{2}\cos(\omega-x) + \frac{1}{2}\cos(\omega+x)$
Modulation is a class of methods to carry information by modifying properties of a wave — amplitude, frequency, phase. For example, a radio station must be able to carry sound of varying amplitudes and frequencies, like music. Since airspace/bandwidth is expensive, we try to encode information in one or more of these properties. In Multiplexing Methods, we describe how to send multiple streams of information across the same time (TDMA), frequency (FDMA), phase, and power (CDMA). 2G/3G encodes 4 bits per wave while 5G may encode up to 10.
This video provides great intuition for different types of modulation.
https://www.youtube.com/watch?v=0faCad2kKeg&pp=ygUXaG93IGNlbGx1bGFyIGRhdGEgd29ya3M=
This is the case we deal with most often — mobile data is analog carrier + digital data.
The earliest/most rudimentary forms of modulation are AM, FM, and PM.
“~” means “is proportional to”
Amplitude Modulation