Fourier Series of 2 Segment Function.

Cuthbert Nyack

The diagram opposite shows a periodic function consisting of 2 segments ab and cd. The height and slope of the segments can be changed by a,b,c,d and the width of each segment can be changed by e and f.
For a flat symmetric pulse, the spectrum falls within a sinc envelope. The frequency of the first zero of the sinc increases as the width of the pulse reduces.
The Fourier spectrum of the pulse can be investigated by the applet below.

The applet below shows the spectrum and reconstruction of a variable width periodic pulse.

parameters a, b, c,d, e, f can be changed by scrollbars 2 to 7.
ns changes the number of terms summed.
t shows the error at any time within a period.
Ev,OddGn(29)changes the gain of the even/odd parts of the spectrum.
MagGn(30) changes the magnitude of the spectrum.
ErrGain(31) changes the gain of the error.

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