Signals in the time and frequency domain - Signals, Processes, and Systems - page 24

Illustration 21: Jean Baptiste FOURIER (1768-1830)
Fourier is regarded as one of the founders of mathematical physics. He developed the foundations of the
mathematical theory of heat conduction and made important contributions to the theory of partial differen-
tial equations. He could not have dreamt of the importance that "his" FOURIER transformation would
have in natural sciences and technology.
Periodic oscillations
These experiments are to be carried out with various periodic oscillations.
Periodic oscillation s are oscillations which are repeated over and
over again in the same way after a specific period length T.
Theoretically - i.e. seen in an idealised way - they last for an
infinite period of time in the past, the present and the future. In
practical terms this is never the case but it simplifies the approach.
In the case of many practical applications - for instance, in quartz clocks and other clock
pulse generators ("timers") or in the case of network AC voltage the length of signal is so
great that it almost corresponds to the ideal "infinitely long". The precision of measure-
ment of time depends largely on how precisely periodic the reference voltage was and is
and how periodic it stays.
Although it is very important for many applications, periodic oscillations are not typical
signals. They hardly provide new information as their future course can be precisely
predicted. The greater the uncertainty about the development of the signal at the next
moment, the greater the information may be that is contained in it. The more we know
what message will be conveyed by a source the less the uncertainty and therefore the
information value. Information often seems associated more with knowledge than with
the idea of uncertainty.