The Symmetry Principle - Signals, Processes, and Systems - page 137

Real

Imaginary

Real

Imaginary

Illustration 99: Spectral representation of periodic signals in the GAUSSian plane

Periodic signals contain the common multiples of their basic frequency only in their spectra. In contrast to
previous cases we now expect many "frequency vector pairs".

At the top you can see a periodic rectangular oscillation with a phase shift of 30 degrees or /6 rad. In

Illustration 31 you can see how rapidly the amplitudes decline with increasing frequency. In this case the
same is true: the lower the amplitude the higher the frequency. A classification with regard to frequency is
thus already possible provided we know the basic frequency.

π

The same is true of sawtooth oscillations with a phase shift of 15 degrees or /12 rad. In this case the

amplitudes change (see Illustration 25 - Illustration 30) in accordance with a very simple law:
Û n = Û 1 /n. The second frequency has therefore only half the amplitude of the first frequency etc.

π