Fourier Transform Rectangular Pulse Reconstruction, RC

Cuthbert Nyack
Here a single rectangular pulse width t and height 1/t is passed through an RC circuit with time constant T = RC. Since the spectrum of the pulse is a sinc function, then the output f(t) can be obtained by finding the inverse of the fourier transform of the output, i.e. evaluating the integral below. The correct limits are + and -inf, the finite limits below are used to obtain a numerical approximation to the output.

Fn = 1 in the applet below illustrates the output obtained by evaluating the integral above. Input rectangular pulse is shown in cyan and output in yellow. Spectrum of the pulse is in red and the reconstructed pulse is reconstructed from the part of the spectrum between the green lines. t is the width of the pulse and Tp1 is the pole of the Circuit. In the frequency domain Tp1 is shown as a white x.
Fn = 2 to 5 show special cases of Fn = 1.
Fn = 6 shows the response of a circuit with 2 poles at Tp1 and Tp2.
Fn = 7 to 10 show special cases of Fn = 6.
Fn = 11 shows the response of a circuit with 2 poles at Tp1 and Tp2 and 1 zero at Tz1.
Fn = 12 to 16 show special cases of Fn = 11.

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