A dial-up modem was secretly playing a very fast tune to send data
Old telephone lines were built for voices, not for zeros and ones, so computers talked over them by singing. A modem turned pairs of bits into distinct tones, like an instrument with four notes, and played a rapid melody down the wire. The machine at the other end listened and turned the music back into data.
That trick is modulation: changing some property of a steady wave, called the carrier, so that it carries a message. The message might be sound from a microphone, pictures from a camera or a stream of bits from a computer. The word modem itself is short for modulator-demodulator, a box that does the job in both directions.
Carriers exist partly for a practical reason. To catch a radio wave efficiently, an antenna should be about a quarter as long as the wavelength, and for low-frequency signals that would mean structures kilometres long. Shifting the message up onto a higher-frequency carrier shrinks the antenna to something buildable. Carriers also let many channels share one medium: cable television sends each channel on its own carrier frequency down a single cable, and because they sit at different frequencies they do not collide.
The oldest methods were analogue. In AM radio, the strength of the carrier rises and falls with the sound; in FM, its frequency wobbles instead. Digital schemes pick from a fixed menu of possible states, each standing for a group of bits. Frequency-shift keying switches between set frequencies, phase-shift keying between set phases, and quadrature amplitude modulation varies phase and strength together to pack more bits into each symbol, which is why Wi-Fi, cable systems and LTE rely on it. OFDM goes further, spreading data over many closely spaced sub-carriers.
The arithmetic is simple. In that four-tone modem, playing 1,000 tones a second is a rate of 1,000 baud, but since each tone carries two bits, the data flows at 2,000 bits per second. A menu of 16 symbols carries four bits apiece, quadrupling the data rate for the same number of symbols.
Source: Signal modulation
