1. Ultrashort Pulse

2. Pulse Wave

## Every function

can be represented by the summation of individual

## frequency components

,
the so called

## Fourier Series

. With a set of given single frequencies a new time signal can be generated.

On the other hand by

## sampling

a time signal with respect to its frequency components, the

## source frequencies

of the time signal can be revealed. This process is known under the term

## Fourier Transformation

and widely used in
engineering and science.

The

## interactive visualization

on this pages exemplifies the Fourier Transformation and its
characteristic parameters. The Graphs show; the resulting or starting time signal (top), the single frequency terms (bottom-left)
and the spectral representation of the frequency components (bottom-right). The blue lines in the spectrum indicate the individual frequencies
(

## Delta Dirac Functions

); the connecting dark line is (spline-) interpolated.

The Fourier Series for generating a rectangular function or pulse train is shown below.
The parameters

## Pulse-Period T

,

## Pulse-Width

and

## n-Number of Frequencies

can be set by the sliders above.