Fourier Series Applet of Double Pulse Function.

Cuthbert Nyack

The function opposite shows a double pulse. Its spectrum falls within a wavepacket envelope and has an appearance similar to the familiar 2 slit interference pattern.

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

Fn Changes the function of the applet.
Fn = 1 shows the double pulse. The reconstructed waveform is in green, cyan and pink shows the even (f(t) = f(-t)) and odd (f(t) = - f(-t)) parts of the pulse.
Fn = 2 to 12 show special cases of Fn = 1.

Parameters a, b, c, d, e, f, g, h can be changed by scrollbars 2 to 9.
ns changes the number of terms summed.
t shows the error at any time within a period.
Ev,OddGn changes the gain of the even/odd spectrum.
MagGn changes the gain of the magnitude spectrum.
ErrGain changes the gain of the error.

Fn = 13 shows the double pulse. The reconstructed waveform is in green, pink magenta and blue shows the half wave symmetric(f(t) = - f(t + T/2)) and asymmetric (f(t) = f(t + T/2)) parts of the pulse.
Fn = 14 to 20 show special cases of Fn = 13.
Fn = 21 shows the expression used for the Fourier Series.

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