Fourier Transformation: Pulse Wave

Switch to Ultrashort Pulse

The Fourier Series for generating a rectangular function or pulse train is shown on the right. The parameters

Pulse-Period T




n-Number of Frequencies

can be set by the sliders above.

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


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. Choose one of the following examples:

1. Ultrashort Pulse 2. Pulse Wave

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