Fourier Series Applet, Reconstruction of Parabolic and Cubic wave.

Cuthbert Nyack

Integrating a triangle wave produces a parabolic wave with equation:-

and the Fourier Series which converges as 1/n**3 is.

Integrating a parabolic wave leads to the following cubic wave given by:-

and with a 1/n**4 Fourier Series representation.

The applet below shows the reconstruction of a parabolic and cubic wave from their Spectrum. Fn = 0 shows the reconstruction of a parabolic wave and Fn = 1 shows the reconstruction of a cubic wave.
ns changes the number of terms summed.
t shows the error at any time within a period.
eok, mk changes the gain of the even/odd, magnitude spectrum.
ek changes the gain of the error.

Going from a square wave to a triangle to a parabolic to a cubic wave is equivalent to approximating a sinusoid by a constant, straight line, quadratic or cubic approximation.

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