Signals in the time and frequency domain - Signals, Processes, and Systems - page 33

Illustration 30: Doubling frequency
Here the period length of the sawtooth signal is T = 0.5s (or for example 0.5 ms). The frequency of the
sawtooth signal is accordingly 2 Hz (or 2 kHz). The distance between the lines in the amplitude and phase
spectrum is 2 Hz (or 2 kHz). Note the changed phase spectrum. Although it is an oversimplification it is
possible to say: our eyes see the signal in the time domain on the screen of the oscillograph but our ears
are clearly on the side of the frequency domain.
As we shall see in the case of many practical problems it is sometimes more useful to con-
sider signals sometimes in the time domain and sometimes in the frequency domain.
Both ways of presenting this are equally valid, i.e. they both contain all the information.
However, the information from the time domain occurs in a transformed form in the
frequency domain and it takes a certain amount of practice to recognise it.
Apart from the very complicated (analogous) "harmonics analysis" measurement
technique there is now a calculating procedure (algorithm) to compute the frequency-
based way of presentation - the spectrum - from the time domain of the signal and vice-
versa. This method is called the FOURIER transformation. It is one of the most important
signal processes in physics and technology.
FOURIER Transformation (FT):
Method of calculating the (frequency) spectrum of the signal from
the progression in time .
Inverse FOURIER Transformation (IFT)
Method of calculating the progression of a signal in time from the
spectrum.