# Transcript

ALLAN JONES
Hello. I’m Allan Jones, and I helped to put together this short course in communications. Throughout the course, I'll be talking to people who’ve contributed in one way or another. The first contributor is Helen Donelan, who was the main author of the material in Section 1. Hello, Helen.
HELEN DONELAN
Hello.
ALLAN JONES
A fundamental concept in telecommunications is the sine wave and also the cosine wave. What are these?
HELEN DONELAN
Oh, well, sine and cosine waves are really the same as each other. They’re a type of smooth, repeating waveform. And they will generally represent the way many natural phenomena vary in time and space. They have this characteristic smooth undulating shape which repeats itself.
You can turn them into sound. And if you do, they have a very characteristic sound that people often describe as pure. This is an example.
[BEEP]
This is a bigger one.
[LOUDER BEEP]
This is one where the shape is repeating slowly.
[LOWER-PITCHED BEEP]
Finally, this is one that repeats very rapidly.
[HIGH-PITCHED BEEP]
The light from a very pure source, like a laser, would be sinusoidal. And by that, we mean it has the shape of a sine or a cosine wave, if you could see its variations. Radio waves have the same shape prior to modulation. Sine waves also are related to rotation. So the voltage from a rotating generator of electricity fluctuates with the shape of a sine wave.
ALLAN JONES
Why are these waves so important in the context of communications?
HELEN DONELAN
Well, at the basic level, signals can be discussed in terms of the properties of sine waves, the three main properties being frequency, amplitude, and phase. So signs and cosines are the basis of a lot of the vocabulary that we use.
But the importance of sine waves does go beyond that. You can combine sine waves to create almost all common periodic wave shapes, for example, the square wave, which can be used to represent digital data. So it can be helpful to think of complicated waves, such as a square wave, in terms of the sine waves that you’ve combined to make the wave, so adding different sine waves to make that more complicated wave.
So for example, any wave with sharp corners or sudden transitions, going back to the square wave again, contains a lot of high frequency sine waves. We know that because when you synthesise that sort of wave from sine waves, you find it’s high frequency sine waves that give you the sharp corners and the sudden transitions.
ALLAN JONES
OK, so maybe that answer has a bearing on my next question. In this subject, people often use the terms time domain and frequency domain. For instance, they might talk about the time domain representation of a signal. And this might be contrasted with its frequency domain representation. What do these terms mean?
HELEN DONELAN
Well, the time domain representation is the one that we’re probably most familiar with. So if you think back to the square wave again, maybe representing alternating ones and zeros in digital data, then the wave is that one for a period of time. Then it drops to a zero, and then it goes back to a one, and so on. And this is what we mean by the time domain description of a signal.
What you can do is think of the same square wave in terms of the sine waves and their frequencies that you would need to add together in order to synthesise it. So those sine waves and the proportions in which they are combined will be the frequency domain representation of a square wave.
One representation is sometimes more useful than the other. So for example, if you phone a bank or another business, often the first thing you get is a series of recorded questions where you have to answer yes or no or maybe say your date of birth. At the other end, there's a speech recognition system. What this is usually doing is analysing your response in the frequency domain. And it does this by looking at how the power in your speech is distributed in different frequency bands. This is how it works out what syllables it is you are saying.
ALLAN JONES
Thanks.