Fourier Series Spectrum of Pulse and Waveform Reconstruction

Cuthbert Nyack
In this page, the Fourier series is used to reconstruct a periodic triangular pulse.
The pulse f(t) is shown opposite. It has a discontinuity in f(t) at t = +T/4 a discontinuity in the derivatives of f(t) at t = 0. In this case the pulse is neither even or odd so both coeffients an and bn in the Fourier series must be calculated.
A plot of the even coefficients an and the odd coefficients bn is shown opposite.

The applet below shows the reconstruction of a triangular pulse.

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.
Fn = 1 to 4 shows the reconstruction of modified pulses.

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COPYRIGHT © 1996 Cuthbert Nyack.