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

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

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.

COPYRIGHT © 1996 Cuthbert Nyack.