Radio & TV - Math Matters - Maplesoft

### Math Matters

Signal processing is one of the most important mathematical fields that supports the design and effective operation of radio and TV.

Amplitude Modulation (AM) is the earliest form of radio transmission. It applies a simple combination of a carrier wave and a modulating wave (the message). For example, a carrier wave is,

The signal that we wish to broadcast could be

The modulated signal is then

Frequency Modulation (FM) uses the modulating signal to vary the frequency of the carrier signal. FM signals are generally more robust and are capable of carrying higher fidelity signals.

Claude Shannon (American, 1916 – 2001) introduced Information Theory in 1948. Information Theory mathematically predicts the amount of information contained in a signal and the ability of a channel to transmit this information. One of his equations states that the capacity of a channel (how much information can be transmitted) is given by

where B is the channel bandwidth and S/N is the signal-to-noise ratio of the channel. This type of analysis was instrumental in improving the quality of communication systemsand even other branches of computer science and engineering, such as image processing, data mining, and pattern recognition. Today we see Shannon’s legacy in virtually all aspects of the Information Revolution.

Guglielmo Marconi
(Italian, 1874-1937)
was the first to successfully transmit radio signals across the Atlantic Ocean using a telegraph, in 1901.