Fourier-Zeichnung

Vorlage:

Fourier-Ordnung:

Parametrisierung: Zeichnung für Fourier-Analyse schließen Schließungsanteil:

Anzeige: Ursprüngliche Kurve Fourier-Rekonstruktion Schließung Epizyklen

Epizyklen animieren Periode (s): t: 0.000 Skalierung:

Information & Mathematik

Kurze Erläuterungen zur aktuellen Kurve und ihrer Fourier-Darstellung.

Positive Frequenzen liegen oberhalb, negative unterhalb der Nulllinie; der Abstand zeigt den Betrag des Koeffizienten.

Bewegen Sie den Zeiger über einen Balken oder klicken/tippen Sie auf einen Koeffizienten.

Coefficient Lab (experimental)

Experiment with the calculated coefficients. The input curve is unchanged; transformations remain active until reset.

Operation order: derivative → center → reverse → frequency filter → smoothing → manual zero mask → magnitude threshold.

Fractional derivative / integral

Enabling this mode sets c₀ to zero. At j = 1 the curve is differentiated; at j = −1 it is integrated with zero mean.

Shape and frequency filters

Position and traversal

Center at origin (remove c₀)

Removes the mean complex position by setting c₀ to zero.

Reverse traversal

Swaps cₖ and c₋ₖ: same geometric path, opposite traversal direction.

Frequency filters

The Fourier-order control already sets the highest available frequency. These filters select subsets of that spectrum.

Frequency selection

Smooth the curve

Gradually suppress higher frequencies with a Gaussian envelope. The strength is relative to the currently available maximum order.

Smoothing strength 0%

Coefficient cleanup

Remove insignificant coefficients

Set coefficients below a percentage of the largest remaining magnitude to zero.

Magnitude threshold 0%

Zero selected coefficients

Enable selection mode, then click or tap any number of stems in the spectrum above.

No coefficient transforms active.