The field of communications spans a range of applications from high-level network management down to sending individual bits down a channel. The Fourier transform is usually associated with these low level aspects of communications.

If we take simple digital pulse that is to be sent down a telephone
line, it will ideally look like this:

If we take the Fourier transform of this to show what frequencies make up this signal we get something like:

This means that the square pulse is a sum of infinite frequencies. However if the telephone line only has a bandwidth of 10MHz then only the frequencies below 10MHz will get through the channel. This will cause the digital pulse to be distorted e.g.

This fact has to be considered when trying to send large amounts of data down a channel, because if too much is sent then the data will be corrupted by channel and will be unusable.

Extending the example of the telephone line, whenever you dial a number on a " touch-tone " phone you hear a series of different tones. Each of these tones is composed of two different frequencies that add together to produce the sound you hear.

The Fourier transform is an ideal method to illustrate this, as it shows these two frequencies e.g.

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