Fourier Transform Rectangular
Pulse Reconstruction, RC
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
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.
Return to main page
Return to page index
COPYRIGHT © 2000, 2012 Cuthbert Nyack.