1D Example

Lets consider a 1D (e.g. Audio) example to see what the different domains mean:

Consider a complicated sound such as the noise of a car horn. We can describe this sound in two related ways:

• sample the amplitude of the sound many times a second, which gives an approximation to the sound as a function of time.
• analyse the sound in terms of the pitches of the notes, or frequencies, which make the sound up, recording the amplitude of each frequency.

In the example below (Fig ) we have a signal that consists of a sinusoidal wave at 8 Hz. 8Hz means that wave is completing 8 cycles in 1 second and is the frequency of that wave. From the frequency domain we can see that the composition of our signal is one wave (one peak) occurring with a frequency of 8Hz with a magnitude/fraction of 1.0 i.e. it is the whole signal.

Relationship between Time and Frequency Domain