Summary

Elements of a communication system: every system is built from a transmitter (prepares and sends the message), a channel (the physical medium, which attenuates and adds noise), and a receiver (recovers the message).

Need for modulation: a message signal must be shifted onto a high-frequency carrier before transmission, because of the impractical antenna size, negligible radiated power, and mutual interference between signals that direct, unmodulated transmission would otherwise require.

Amplitude modulation (AM): the carrier's amplitude is varied in step with the message; $c_m(t)=[A_c+A_m\cos(\omega_m t)]\cos(\omega_c t)$; modulation index $\mu = A_m/A_c = (A_{max}-A_{min})/(A_{max}+A_{min})$; bandwidth $=2f_m$.

Frequency modulation (FM): the carrier's frequency (not amplitude) is varied in step with the message; needs a larger bandwidth than AM for the same message, but is far more resistant to (amplitude-type) noise, since a limiter stage can strip out amplitude disturbances before demodulation.

Bandwidth of signals: speech $\approx 2800$ Hz; music $\approx 20$ Hz-20 kHz; TV video $\approx$ a few MHz (a complete channel $\approx 6$ MHz including sound and colour); digital data bandwidth rises with bit rate.

Bandwidth of transmission medium: twisted pair (of the order of 1 MHz) < coaxial cable (hundreds of MHz) $\ll$ optical fibre (into the terahertz range); free-space bandwidth set by the allotted radio band. …