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# Fourier Analysis

A periodic signal satisfying the Dirichlet condition can be described by a Fourier analysis as a Fourier series, i.e., as a sum of sinusoidal and cosinusoidal oscillations. By reversing this procedure a periodic signal can be generated by superimposing sinusoidal and cosinusoidal waves. The general function is:

The Fourier series of a square wave is

or

The Fourier series of a saw-toothed wave is

The approximation improves as more oscillations are added.

No Java, no applet! Sorry! But it would look like this:

The source code (version 1996/07/15) is available according to the GNU Public License.

# Dirichlet Condition

The Fourier series of a periodic function x(t) exists, if
1. , i.e., x(t) is absolutely integratable,
2. variations of x(t) are limited in every finite time interval T and
3. there is only a finite set of discontinuities in T.

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