Signals in the time and frequency domain - Signals, Processes, and Systems - page 35

Illustration 32: Pulse form without rapid transitions
Within the (periodic) sequence of GAUSSian pulses each pulse begins and ends gently. For this reason the
spectrum cannot contain any high frequencies. This characteristic makes GAUSSian pulses so interesting
for many modern applications. We will come across this pulse form frequently.
Example: a periodic sawtooth of 100Hz only contains the sinusoidal components
100 Hz, 200 Hz, 300Hz etc.
The spectrum of periodic oscillations/signals accordingly always consists of lines at equal
distances from each other.
Periodic signals have line spectra!
The sawtooth and square wave signals contain steps in "an infinitely short space of time"
from, for example 1 to -1 or from 0 to 1. In order to be able to model "infinitely rapid
transitions" by means of sinusoidal signals, sinusoidal signals of infinitely high frequency
would have to be present. Hence it follows:
Oscillations/signals with step function (transitions in an infinitely
short period of time) contain (theoretically) sinusoidal signals of
infinitely high frequency.