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
The Fourier series of a saw-toothed wave is
The approximation improves as more oscillations are added.
The source code (version 1996/07/15) is available
according to the GNU Public License.
The Fourier series of a periodic function x(t) exists, if
i.e., x(t) is absolutely integratable,
- variations of x(t) are limited in every finite time interval
- there is only a finite set of discontinuities in T.